hsc physics in month
TRANSCRIPT
Neville Warren
MSc, DipEd, MACE
PASCAL PRESS
Copyright © 2002 Neville Warren
ISBN 1 877085 12 X
Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au
Publisher: Vivienne Petris Joannou Editor: May McCool Typeset by Precision Typesetting Services, Sydney Cover by DiZign Printed in Singapore by Green Giant Press
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The total time allocated is approximately 22 hours. This includes 13 hours for the three core topics, approximately 5 hours for the option topic (depending on the topic), three hours for the exam and an hour to go through the answers. To revise in a month you will need to keep to a schedule.
For example, you might choose to follow the following timetable.
Space Gravity Space Launch and
Return Future Space Travel Special Relativity Motors and
Generators The Motor Effect E lectromag netic
Induction
Electric Generators Transformers Electric Motors From Ideas to Implementation
Cathode Rays Quantum Theory Solid State Devices Su percond uctivity
Do ONE option from
the following: Medical Physics Astrophysics Quanta to Quarks
Sample Examination (3 hours)
Check answers (1 hour)
Check that you know the key points in each topic that you are studying. This quick test should take only 10 minutes to complete. Check your answers by referring to the bottom of the page. This is important feedback for you.
If you got any of the test questions wrong, you can quickly find an explanation and more information on this question by going to the same number in this section. You should also read the other key points for this topic to help you revise thoroughly.
These are exam-style questions that you should be able to answer in order to prepare for the exam. In this section you apply your knowledge. Make sure you have fully revised your work in the Key Points section. Complete answers are found at the back of the book. Hints to some questions are provided in case you need extra help with them. They are found at the bottom of the page. Marks are allocated for each question. Always check the marks and use them as a guide for how much to write in your answer.
When you have completed all sections you are ready to complete the exam paper. Set aside the required time and try to do it under exam style conditions - this way you will benefit most from it.
Complete answers are provided for each question.
Mark your paper to see how well you have done.
Tips for the HSC exam can be found on the inside back cover.
A suggested time is given for each section. Try to follow it.
A week-by-week time plan for the month is given on the contents page to help you plan your study timetable.
A force F acts between two masses separated by a distance d. If the masses are both doubled and their separation is halved, the new force is now:
F 2F 4F 16F
Surrounding any object with mass is a ____ field.
The gravitational field strength of a mass m placed a distance r from the mass is g. If the distance from the mass is halved, the new gravitational field strength is:
g/4 g/2 2g 4g
The acceleration due to gravity near the Earth's surface is approximately equal to ____ m.s-2.
____ is the force on an object due to a gravitational field.
The acceleration due to gravity on Mars is 3.8 m.s-2. The weight of a 10 kg mass on Mars is:
38 m.s-2 38 N 0.38 N 10 N
The mass of an object on Earth is 5 kg. Its mass on Mars (where the acceleration due to gravity is 3.8 m.s-2) is:
5 kg 5 N 19 kg 19 N
When a force is applied to a mass and the mass moves through a distance, we have done on the mass. If this force is used to move the mass vertically, we have increased the mass's ___ _
The gravitational potential energy has its zero value at ___ _
The gravitational potential energy Ep of an object of mass m placed a distance r from the Earth (mass ME) is given by:
Ep =_G mME r
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Every mass exerts a force of attraction on every other mass in the universe in accordance with Newton's law of universal gravitation. This states 'the force, F, between two masses m, and m2 whose centres are separated by a distance r is proportional to the product of their masses and inversely proportional to the square of their separation'.
Mathematically F = G m1m2
r2 A gravitational field surrounds the Earth. This field exerts an attractive force on objects on it and around it.
The gravitational field strength, 9, of a mass m at a distance r from the mass is
given by: 9 = Gm. On Earth 9 is equal to -9.8 N.kg-'. r2
The gravitational field strength is numerically equivalent to the acceleration due to gravity. On Earth, this is equal to -9.8 m.s-2.
Weight is the force on an object due to a gravitational field.
The weight Wof a mass m on a planet where the acceleration due to gravity is 9 is given by W= mg
The mass of an object is independent of its location. Its weight, however, depends on where it is placed. For example a 10 kg mass has a weight of 98 N on the Earth but only 38 N on Mars (where 9 = 3.8 m.s-2). Its mass, however, is 10 kg on both planets.
As we lift an object from the ground to a height above the ground we do work on it. This work is stored in the object as gravitational potential energy.
The gravitational potential energy is a measure of the work done in moving an object from infinity (that is, a very large distance away) to a point in the field. At infinity, the gravitational potential energy is defined to be zero.
The gravitational potential energy of an object of mass m placed a distance rfrom the
Earth (mass ME) is given by Ep = -G mME • The negative sign comes about because of
r where we define the zero of potential energy to be.
CHECKLIST - Can you: 1. Calculate the force between two masses using Newton's law of universal gravitation? 2. Define weight? • 3. Determine the weight force for a body on Earth and on other planets? 4. Describe an experiment to determine the acceleration due to gravity? 5. Define gravitational potential energy?
Four planets alpha, beta, gamma and delta are shown in the figure below.
alpha
Radius r Mass M
beta
Radius r Mass 2M
gamma
Radius 2r Mass M
The planet with the largest acceleration due to gravity is: alpha beta gamma delta
delta
Radius 2r Mass 2M
The weight of a body on Earth is 2000 N. What is its weight on Mercury (where g = 3.4 m.s-2)?
The gravitational potential energy of a mass near the Earth is negative. This means: no work needs to be done to move the mass to infinity no work needs to be done to move the mass from infinity the gravitational potential energy at infinity is zero the gravitational potential energy at infinity is positive.
What is the gravitational potential energy of a 1000 kg satellite in low Earth orbit 300 km above the Earth's surface? (The radius of the Earth is 6380 km and its mass is 5.983 x 1024 kg)
As part of your course you determined a value for the acceleration due to gravity. Clearly explain how you did this and account for any variation from the accepted value of 9.8 m.s-2.
A ____ is any object moving only under the influence of gravity.
_____ motion can be best analysed by breaking it into two components. The horizontal component is motion with constant . The vertical component is motion with constant ___ _
Two objects are released from the same height. Object A falls straight down and object 8 follows a curved path as shown in the figure. It is true that:
8 hits the ground before A A hits the ground first only if it is heavier than 8
~" ObjectB A hits the ground before 8 ! (Jf!&i Object A
A and 8 hit the ground at the same time. Falling masses
The equations linking the horizontal displacement x, the horizontal component of velocity vx' the time t, the acceleration due to gravity ag and the vertical displacement 11y, are given by x = and 11y = . The path followed by a projectile has the shape of a ___ _
The minimum velocity required for an object to leave the gravitational pull of a planet is called its velocity. This is of the mass of the object leaving the planet. Newton was the first to propose the idea of artificial ___ _
The acceleration of an object moving in a circular path with constant speed is directed towards the of the circle. Astronauts in spacecraft and patrons of fun park roller coasters both experience significant ___ _
As a rocket is launched, fuel is burned and the resulting are expelled downwards. Conservation of results in the rocket moving up. As the fuel is consumed, the acceleration . Rockets fired into space are fired in a/an _____ direction to take advantage of the Earth's ___ _
The orbit of a satellite with a period of 24 hours is called a orbit.
Low Earth orbit satellites travel faster than satellites further from the Earth. True or false? ___ _
The movement of spacecraft through the solar system is aided by using 'gravity-assist trajectories', also called the effect. Safe re-entry of spacecraft to Earth is restricted to a narrow ____ _
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A projectile is any object moving under the influence of gravity only. Examples include a golf ball after it has been hit, artillery shells fired from guns, 'dumb bombs' dropped by warplanes '"
Projectile motion is composed of two independent motions: a horizontal component with constant velocity and a vertical component with constant acceleration.
The independence of the two components of projectile motion is easily illustrated as shown in the figure on the right. The two objects fall at the same rate and hit the ground at the same time regardless of the horizontal motion.
::
c
The independence of motions The horizontal motion is described by D.x = uxt; the vertical
motion is described by .6.y = ~age. The curved path followed by a projectile is called its
trajectory. This curve is a parabola.
The escape velocity is the velocity needed for an object to escape from the Earth (or other planet or moon). It depends on the radius and mass of the planet and the
gravitational constant according to vescape = ~2GME . It follows that as the mass ofthe RE
planet increases, the escape velocity increases; similarly as the radius decreases, the escape velocity increases. It is independent of the mass of the object trying to escape.
Newton first proposed the idea of artificial satellites. He reasoned that if a cannon was fired horizontally from a high mountain, a speed could be reached where the shell would go into orbit around the Earth.
The motion of an object in a circular path of radius r with Artificial satellites constant speed v is called uniform circular motion. For an
?
object moving with uniform circular motion, the centripetal acceleration ac is directed 2
towards the centre of the circle and is given by ac =~. For a satellite orbiting the r
Earth, the centripetal force is supplied by the gravitational attraction of the Earth to the satellite.
g-forces are measured in units ofthe Earth's gravitational acceleration, g. They arise whenever there are accelerations, such as in rocket launches and roller-coaster rides. Humans can withstand accelerations up to -10g when the acceleration is directed parallel to a line drawn between the person's front and back. Early astronauts experienced these forces as they reclined in specially moulded chairs. In today's Space Shuttle the g-forces are limited to -3W.
mg
Roller coaster ride
Consider a roller coaster ride as shown. As the rider moves through a bottom curve, the reaction force of the seat up on the rider must supply the necessary centripetal force, that is:
mv2
N-mg=-R
mv2
N=mg+-R
The g-forces are found from the 'normal force' divided by the weight. That is:
9 felt by rider = ~ mg
mv 2 mg+--
_ R mg
v 2
=1+gR
It can be seen that the g-forces increase as the speed increases and/or the radius of the curve decreases.
Rockets are placed into Earth orbit by launching the spacecraft vertically and then tilting the trajectory parallel to the Earth's surface when the correct orbital speed is reached. By tilting in the easterly direction scientists can take advantage of the Earth's rotation (from west to east).
A geostationary orbit is one in which the satellite has a period of 24 hours. If the orbit is in the equatorial plane, the satellite appears to stay above the same point on the Earth. Satellites placed in geostationary orbits allow communication signals to be 'bounced' around the world.
Kepler's laws describe the motion of satellites according to r: = G~ . For a constant T 4n
mass it follows that as the radius decreases, the period must also decrease. Consequently the speed must increase so satellites in low Earth orbits travel faster than satellites further out in space.
'Gravity-assist' trajectories (also called the 'slingshot' effect) are used to send space probes to distant planets. A space probe approaching a planet picks up some of the planet's angular momentum resulting in a speeding up of the spacecraft relative to the Sun.
Outgoing velocity spacecraft. Velocity of Venus Outgoing velocity
relative to the Sun. of spacecraft relative
Venus
The incoming speed and the outgoing speed are the same relative to Venus (but direction is changed).
~ ~~ to Venus.
Outboun~ velocity relative to the Sun.
Velocity of Venus relative to the Sun.<III<!III(IIII----
Venus
Venus moves around the Sun. The spacecraft gains most of Venus s
Incoming velocity velocity through gravitat" nal of spacecraft. attraction.
Gravity-assist trajectories
Incoming velocity of spacecraft relative to the Sun.
Safe re-entry to Earth is limited to a small 'window'. This ensures that the spacecraft does not 'bounce' off into space if it comes in too shallow and the g-forces are not too high for the astronauts if it comes in too steep. It also means that the heat from re-entry is not too high. The Space Shuttle uses a variety of materials capable of withstanding the tremendous temperatures, as high as 1300°C. The 'allowed' angle of re-entry is -6.2° ± 1 ° relative to the Earth's horizon.
CHECKLIST - Can you:
Re-entry corridor
5.20
Re-entry 'window'
7.20
1. Analyse and solve problems of projectile motion in terms of its horizontal and vertical components? 2. Explain the concept of escape velocity and discuss the factors that affect it? 3. Analyse the forces involved in uniform circular motion? 4. Compare g-forces on astronauts and roller coaster riders? 5. Analyse the acceleration of a rocket during launch? 6. Compare low Earth orbits with a geostationary orbit? 7. Describe the slingshot effect used to assist space probes? 8. Relate Newton's laws to the motion of satellites. 9. Discuss issues associated with safe re-entry of spacecraft to Earth including the optimum angle for
re-entry and the consequences of not achieving this? 10. Describe the contributions of Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O'Neill or von Braun to
space exploration?
A projectile is fired with an initial speed of 500 m.s-1 at an angle of 30° to the ground. Find:
the maximum height reached by the projectile the time to reach the maximum height the distance travelled horizontally.
The escape velocities for Earth and Mercury are shown in the table below.
Planet Earth Mercury
Escape 11.2 km.s-1 4.3 km.s-l velocity
What is meant by escape velocity? What factors affect the escape velocity?
The period of revolution of the Martian moon Demos is 1.09 x 105 s. What is the radius of its orbit given that the mass of Mars is 7.1 x 1023 kg?
Describe the changes that occur in a rocket/s acceleration as it is launched into space. Be sure to explain the causes of the accelerations and the causes of any changes.
Astronauts in the Space Shuttle experience forces up to 3Wwhere W is the weight of the astronaut. Explain how it is possible for riders in a roller coaster to experience similar forces.
Current rockets work by ejecting _____ formed by the combustion of a ___ _ and oxygen. Conservation of means that the rocket will move in the opposite direction to the exhaust ____ _
Scientists have been able to manufacture spacecraft that are able to travel at hundreds of thousands of kilometres per hour. True or false? ____ _
The relatively ____ speeds of spacecraft mean that travel times to distant planets would be very ___ _
The engines of spacecraft are operating all the time. True or false? ____ _
Three factors that affect communication between the Earth and distant space probes are and ____ _
____ radiation travels at the ultimate speed of 3.0 x 108 m.s-1.
The reduction in strength of microwave signals as they travel through space from distant sources is a result of a/an square law. This weakening of strength is referred to as _________ _
Sunspots are relatively ____ areas on the surface of the Sun. They have magnetic fields thousands of times than the Earth/s magnetic field.
The solar wind consists of: a stream of positive particles a stream of negative particles a stream of positive and negative particles a stream of neutral particles.
The Van Allen radiation belts are two belts of energetic ____ particles. They can be disrupted by intense activity. The resulting storms can affect communication on Earth.
Communication with satellites or other spacecraft relies on electromagnetic radiation in the region of the electromagnetic spectrum.
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Rockets operate by expelling gases formed by combustion of the fuel and oxygen. These are ejected at very high velocities. Conservation of momentum ensures that the rocket travels in the opposite direction to the exhaust gases.
Scientists are not yet able to produce speeds of spacecraft more than a few tens of thousands of kilometres per hour. For example, the 1969 Mariner 6 space probe to Mars took 157 days to travel 92,800,000 km, an average speed of -25,000 km.h-1.
The relatively slow speeds of spacecraft mean that travel times to even the closest planets are long. A round trip to Mars for example, would take up to two years and eight months. Currently, extended manned space travel is not feasible.
The engines of spacecraft are designed for manoeuvring the spacecraft, to bring it into orbit around a planet (or moon), and in the most extreme situation, of leaving the planet (or moon). At all other times they are turned off.
Distance, the Van Allen radiation belts and sunspots affect communication between the Earth and distant space probes.
Even though electromagnetic radiation travels at the enormous speed of 3.0 x 108 ms1, nevertheless the time for a signal to travel from distant objects is not insignificant, especially for very distant objects. For example, it takes 4 years for light to travel to us from our nearest star (other than the Sun).
The intensity of the electromagnetic radiation decreases as the square of the distance from the source (an inverse square law). This loss of signal strength is referred to as space loss. The dimensions of space are so vast that the electromagnetic energy able to be detected from distant objects (be they emissions from a spacecraft with a relatively low power transmitter or those from a star), are tiny.
Sunspots are relatively cool areas on the surface of the Sun with strong local magnetic field strengths some thousands of times stronger than the Earth's magnetic field. Sunspots vary in activity. In an eleven-year cycle, the number of sunspots varies from a minimum up to a maximum and back to a minimum.
Sunspots are also associated with the solar wind. This wind consists of a stream of charged particles, mostly protons and electrons that flow out from the Sun in all directions at a speed of -400 km.s-1. The number of these particles increases following increases in sunspot activity. The solar wind affects the Earth's magnetic field and this in turn affects radio communication.
The Van Allen radiation belts are two belts of energetic charged particles, mainly electrons and protons, lying at right angles to the equator of the Earth.
Solar wind particles (as well as particles from interactions between the Earth's upper atmosphere and energetic cosmic rays) become trapped in the Van Allen radiation belts. Intense solar activity can disrupt the belts. This in turn is associated with auroras and magnetic storms which can lead to interference of short wave radio communication, errors in communication satellites and even failure of electrical transmission lines.
Inner belt
Van Allen radiation belts
Communication with satellites and other spacecraft relies on electromagnetic radiation in the radio frequency part of the electromagnetic spectrum. In particular, microwaves in the frequency range 1000 MHz to 300,000 MHz are the major carriers of data between earthbound stations and between Earth stations and satellites and space probes.
CHECKLIST - Can you: 1. Explain how space travel is limited by the current maximum speed of spacecraft? 2. Describe the factors affecting reliable satellite communication?
What is the most significant problem making extended space travel not feasible at the present time? Clearly explain your answer.
Communication with space probes to distant planets such as Mars is not instantaneous but is always delayed. Explain why this delay occurs. (The distance to Mars is -8 x 107 km.)
The Van Allen radiation belts surround the Earth. What are these belts? How do these belts affect communication between Earth and orbiting satellites?
Sunspots can affect the Earth's communication systems. Describe how this occurs.
The medium hypothesised to transmit light was: ether air anaesthetic
The Michelson-Morley experiment was an attempt to measure: the speed of the ether the speed of the Earth through the ether the speed of light.
An example of an inertial frame of reference is: a car accelerating from a set of traffic lights a car travelling in a straight line with constant speed a car travelling around a corner with constant speed.
Einstein hypothesised that the speed of light: is 3.0 x 108 m.s-1 is constant
The laws of physics are the same for all inertial observers. This is the principle of
The current standard of length, the metre, is measured in terms of ___ _
Because space and time are interdependent we speak of four-dimensional ___ _
Two events occur at the same time for a particular observer. To an observer in a different inertial frame of reference, they occur at different times. This is called the lack of
A metre rule, 2 cm wide, moves at a speed of e/2 relative to a stationary observer. What is the length of the rule as measured by that observer? What is the width of the rule?
A clock moves at a speed of e/2 relative to a stationary observer. If 1 hour passes for an observer travelling with the clock, how much time passes for the stationary observer?
Twins A and B are separated at birth. A is sent into space and B remains on Earth. A eventually returns to Earth. A is now:
younger than B older than B the same age as B
Relativity 'allows' for travel into the past. True or false? ____ _
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The ether (also aether) is the medium proposed prior to Einstein to transmit electromagnetic radiation. Its beginnings go back to the ancient Greeks but the idea was also used by Hooke in 1667 and Huygens in 1678 both of whom proposed that luminous objects set up vibrations that were transmitted through the ether like sound waves through air (compression waves). The ether was supposed to permeate all matter as evidenced by the transmission of light through transparent materials.
The Michelson-Morley experiment was an attempt to detect the motion of the Earth through the ether. It used apparatus similar to that in the diagram.
The presence of the ether would mean that light travelling with and against the ether would take a different time to the light travelling across the ether. This difference should be detected by a change in the interference fringes formed when the light rays are recombined. The result was totally unexpected. It showed that the speed of the Earth relative to the ether could not be detected.
A frame of reference is a coordinate
Light source )go
Ether wind
Michelson-Morley experiment
system with respect to which we take measurements. An inertial frame of reference is one moving with constant velocity (or is at rest). A non-inertial frame of reference is one that is accelerating.
As a result of his work on how the laws of electromagnetism should behave in different frames of reference, Einstein proposed that the speed of light is constant and is independent of the speed of the source or observer. He was unaware of the null result of the Michelson-Morley experiment when he made his hypothesis - it simply provided evidence for his theory.
The principle of special relativity is that the laws of physics are the same for all inertial observers. This means that it is impossible to detect motion in an inertial frame simply by doing an experiment in that frame.
The unit of length, the metre is the defined as the distance travelled by light in a vacuum in the fraction 1/299 792 458 of a second. It follows that distance is therefore defined in terms of time.
For the speed of light to remain constant it means that space and time are relative; we speak of four-dimensional space-time.
Two or more events that are simultaneous for one observer are not necessarily simultaneous for observers in different inertial frames of reference. This is called the lack of simultaneity. This can be illustrated by one of Einstein's famous 'thought experiments'.
The length of a moving rod appears to contract in the direction of motion relative
to a stationary observer; I = IO~1- V
2
. The width is unaffected. For an observer moving c2
with the rod, no length (or width) change occurs.
Time in a moving frame appears to be slower relative to a stationary observer. This is
time dilation; t = g. For an observer moving with the clock, no change occurs. 1--
(2
The twin paradox refers to where imaginary twins are born at the same time and one is sent into space while the other remains on Earth. According to special relativity the twin left behind would 'see' the twin sent into space age less. Similarly, the twin in space would 'see' the twin on Earth age slower. This is the paradox: both say the other ages slower. The paradox is resolved when it is noted that the twin sent into space must undergo accelerations to turn around and come back to Earth. He is therefore in a non-inertial frame of reference and special relativity does not apply. (General relativity, which deals with non-inertial frames of reference, indicates that the twin who ventures into space ages less than the one who stays behind.)
Relativity 'allows' for travel into the future but not into the past. Because an astronaut who leaves the Earth ages slower than his/her contemporaries left on Earth, the astronaut will return to Earth in say 100 years of 'Earth time' but maybe only 60 years of 'astronaut time' (depends on the speed of travel). Thus he returns to the Earth's future.
CHECKLIST - Can you: 1. Explain the features of the ether? 2. Describe the Michelson-Morley experiment and explain the implications of the findings? 3. Explain the meaning of an inertial frame of reference? 4. Explain the significance of the constancy of the speed of light c? 5. Explain qualitatively and quantitatively the consequences of special relativity including lack of
simultaneity, equivalence of mass and energy, length contraction and time dilation? 6. Discuss the implications of special relativity for space travel?
Describe, with the aid of a diagram, how Michelson and Morley attempted to measure the speed of the Earth through the ether and the results they obtained.
Einstein first stated the basic premise of special relativity. He said that the speed of light is constant and is independent of the speed of the source of light or of the observer. Using this and Einstein's 'thought experiment' of a simple 'light clock' in a moving train, explain why time dilation occurs.
Muons are unstable short-lived subatomic particles that can be created in the upper atmosphere when cosmic rays collide with air molecules. They have a lifetime of 2.2 ~s (in their reference frame). If they travel at 0.999c, what is their lifetime relative to an observer on Earth?
The speed of light c is constant and is equal to 3.0 x 108 m.s-1. Clearly explain why an object travelling at a speed less than c cannot be accelerated to c.
Explain how special relativity makes it possible for an astronaut to travel 'into the future'. Why is this unlikely to occur?
Moving charges in a magnetic field experience a ____ _
The doughnut shaped region around the Earth where moving charges are trapped is called the radiation belts.
A conductor of length 50 cm is placed at right angles to a magnetic field of strength 10 T. If the conductor carries a current of 2.5 A, calculate the force acting on the conductor.
What is the direction of the force acting on the conductors in the diagrams?
e e e e
X X X e e e etc X X X Current
I~ X magnetic field into page e e e e '0 e field out of the page
X X X e e II II
A 'current balance' can be used to determine the factors affecting the force on a current-carrying conductor in a magnetic field. Which graph below best shows the relationship between the currents and the conductor separation?
d d d 11d
The turning effect of a force is called its ____ _
A single current-carrying coil of wire is placed in a magnetic field, What is the torque on the coil at the instant shown and in which direction will it rotate?
Axis
,.B __ --,.... __ -;C
I Plane of coil is parallel to magnetic field of 0.2 T
Length of AB and CD = 4 cm Length of BC = 2 cm
Electric motors convert _____ energy into _____ energy,
DC electric motors consist of four essential components, They are ____ _ _____ and ____ _
The direction of the current in a simple DC motor is reversed each half cycle by a _____ ring , Current is brought to (and from) this device by carbon
The field structure of a simple DC electric motor can be provided either by ____ _ magnets or current-carrying ____ _
The motor effect is put to good use in devices such as moving _____ meters and
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Moving charges in a magnetic field experience a force. These moving charges interact via their associated magnetic field.
The doughnut shaped Van Allen radiation belts trap charged particles from space. In doing so they protect life on Earth from this dangerous radiation.
A current-carrying conductor in a magnetic field experiences a force given by F = BIl sin 9. This is the motor effect. From the equation it can be seen that the force depends upon: the magnetic induction (B), the current in the conductor W, the length of the conductor (l) and the angle between the field and the conductor (9). When the conductor is parallel to the field (9 = 0°) the force is zero and is a maximum when the conductor is perpendicular to the field.
The right-hand palm rule allows the direction of the magnetic force to be determined. This states that: If the fingers of the right hand point in the direction of the magnetic field (B) and the thumb points in the direction of the conventional current (1) then the palm points in the direction of the B
force (F) as shown.
I
F Two parallel current-carrying conductors exert forces on each other. The force F per unit length L between two wires carrying current I, and 12 respectively separated by a distance d
Right-hand palm rule
in a vacuum is given by ~ =k 1112 . When the currents are in the same direction, the L d
wires attract; when the currents are in opposite directions the wires repel.
Torque is the turning effect of a force and is given by't = Fp where F is the force and p is the perpendicular distance from the axis to the line of action of the force.
A current-carrying coil in a magnetic field experiences a torque given by't = nB1A cos 9. This is put to practical use in electric motors.
Electric motors convert electrical energy into mechanical energy.
DC electric motors consist of an armature (the coi!), field structure (the magnets), commutator and brushes. Current flowing through the armature interacts with the
magnetic field to produce a torque causing the armature to rotate. In the diagram below, the armature would begin to rotate in a clockwise direction (viewed from the commutator end).
Split ring commutator
,. + ~~
Carbon brush
Simple DC electric motor
Armature
A split-ring commutator reverses the direction of the current in the armature sides each half cycle. This allows the armature to continually rotate in the same direction by ensuring that the current always flows in the same direction around the armature. (Without it, the armature would simply come to rest with its plane perpendicular to the plane of the magnetic field.) Carbon brushes take current to and from the armature.
The field structure can be produced by permanent magnets or by current-carrying coils (electromagnets). The latter are generally stronger and so a larger torque is possible. In real motors, the 'pole pieces' that make up the field structure are generally curved. This ensures a steady torque as the armature always lies parallel to the field and so 't = nBIA where n is the number of turns (coils), B is the magnetic induction, I is the current in the armature and A is the area of the coil.
Practical examples ofthe motor effect include moving coil meters and loudspeakers. Current flowing in the meter or loudspeaker interacts with the magnetic field causing movement of the meter pointer or loudspeaker diaphragm. The moving coil meter is the basis of the ammeter and voltmeter.
CHECKLIST - Can you: 1. List the factors affecting the magnitude of the force on a current-carrying conductor in a magnetic
field? 2. Solve problems using F = BII sin e 3. Describe an experiment to demonstrate the motor effect?
4. Use the equation ~ ==k 11c/2
5. Explain the rotation of a current-carrying coil in a magnetic field and use the equation 7: = nB1A cos e 6. Describe the principle of operation of a simple DC electric motor and the purpose of the armature,
field structure, split-ring commutator and brushes? 7. Explain how the motor effect is used in moving coil meters and loudspeakers?
x x x x x x x A charge moves in a magnetic field as shown. The direction of the initial force on the charge x x x x x x x is:
up the page down the page +Q x x x x x x x
into the page out of the page. x x x x x x x
Two parallel current-carrying wires are separated by a distance d and exert a force per unit length of F newtons per metre. If the current in one of the wires is tripled and the separation doubled, the new force is:
3FI8 9FI8 3FI4 3FI2
A rectangular current-B Current
Magnetic carrying coil ABCD is placed in a magnetic field as shown. The side which experiences a force down the page is:
AB BC c CD No side experiences any force since the coil is parallel to the
A
, ----;<---'~ field is perpendicular -~, ~ ? to the plane of
~ /3"/ - '-»> the page. Coil is / 0 parallel to the
/ ~ field.
Axis field.
A rectangular coil, 5 cm x 3 cm, of 1500 turns is placed in a magnetic field of intensity 0.8 T. A current of 0.1 A flows in the coil.
What is the relationship between the coil and the field when the torque is a maximum? What is the maximum torque on the coil? What is the torque when the coil is set at 45° to the magnetic field?
A moving coil meter is shown. Briefly describe the principle of operation of the meter.
scale
N s
Radial magnetic field Soft iron
Fine wire spring
core
The discoverer of the generation of an electric current by a magnet moving near a conductor was Michael ___ _
When the man in 1 above used a magnet and a coil of wire, he found a current was induced as long as there was between the coil and the magnet.
Electromagnetic induction involves the conversion of ____ energy into ____ energy.
Magnetic flux is a measure of the number of lines of force per unit area the number of lines of force per unit volume the number of lines of force.
Another name for magnetic flux is magnetic induction. True or false? ___ _
Faraday's law states that the induced emf is proportional to the rate of change of
Lenz's law is a consequence of the conservation of charge conservation of energy.
conservation of momentum
The direction of the induced current in the diagram is: down the page up the page out of the page into the page
The induced emf in an electric motor: is called the forward emf opposes the supply emf is only present as the motor first starts.
Field out of page
To prevent an electric motor burning out when it is first turned on a ___ _ resistance is placed in series with the motor.
Changing magnetic fields induce circular currents in bulk conducting material.
The currents in Q11 above can be used in induction ____ and in electromagenetic
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Michael Faraday is credited with the discovery of the generation of an electric current in a conductor by a moving magnet.
Coil
Magnet
Galvanometer
Faraday found that when a magnet is pushed into a coil of many turns connected to a sensitive current-measuring device (a galvanometer) a current is produced as long as the magnet is moving relative to the coil. If there is no movement between the coil and magnet, no current is produced. When the magnet is withdrawn from the coil, current is again produced but it flows in the opposite direction to that when the magnet is inserted. Magnet moving towards
a conducting coil
Electromagnetic induction involves the conversion of mechanical energy into electrical energy.
Magnetic flux is a measure of the number of lines of force emerging from a given area as shown in the diagram on the right.
Magnetic flux density is synonymous with magnetic induction. The greater the density of flux lines (also called 'lines of force'), the greater the magnetic field.
Magnetic flux
Faraday's law states that the induced emf is proportional to the rate of change of magnetic flux. That is, the faster the magnetic flux through the circuit changes, the greater will be the emf induced. This can be made to happen by moving the magnet (or coil) faster, and/or increasing the magnetic induction and/or by having more coils.
Lenz's law states that the induced emfis in such a direction that the current it produces opposes its production. This is a consequence of the law of conservation of energy. If the emf (and its associated current) aided the production instead of opposing it we could create an infinite amount of energy from a finite amount of work - we would effectively get 'something for nothing'. This would violate energy conservation.
The direction of the induced current can be found by the right-hand palm rule.
When a motor is operating it involves relative motion between a conductor and magnetic field and so it produces a back emf. This opposes the supply emf and limits the current flowing in the motor. This in turn limits the speed of the motor - the motor is self-regulating.
When an electric motor is starting, the back emf will be small and so the current in the coil from the supply will be large. (Remember that the back emf opposes the supply voltage.) To keep the current within manageable limits to prevent it burning out the motor, a starting resistance is
Fingers
Thumb points in direction of induced current
point in l direction .*-;~=±==7 -? of magnetic _ field
Palm points in direction of opposing force
Right-hand palm rule
placed in series with the coil. As the coil speeds up (and hence the back emf increases) the starting resistance can be decreased and eventually removed.
Circular eddy currents are induced in bulk conductors in the presence of changing magnetic flux. These eddy currents obey Lenz's law. They also represent a waste of energy as they cause heating of the conductor.
Eddy currents are put to good use in induction cookers and in electromagnetic braking. AC flowing in coils placed below a glass-ceramic cook top induces eddy currents in the metal pans placed on top, heating the pan and its contents. In certain modern trains, electromagnets are brought near to the moving metal wheels inducing eddy currents in the wheels. These currents flow in a direction to oppose their cause in agreement with Lenz's law. This provides a retarding force on the wheels that stops the wheels (and hence the train). Braking is very smooth since the force is greatest when the wheels are turning fastest and gets less as the speed of the wheels gets less.
CHECKLIST - Can you: 1. Describe Faraday's discovery of electromagnetic induction? 2. Define magnetic flux, magnetic flux density and magnetic induction? 3. Qualitatively and quantitatively describe Faraday's law? 4. Explain the cause of Lenz's law and relate this to back emf, eddy currents and electromagnetic
braking?
Below is a schematic diagram of a simple experiment to illustrate electromagnetic induction, similar to one that you could do at school. Explain what is required for a current to be induced and give three ways in which the induced current can be made larger (assuming you had access to additional equipment). Explain your reasoning.
Coil
Magnet
Galvanometer
A physics teacher was overheard telling a class that 'Lenz's law is simply a consequence of energy conservation'.
What is Lenz's law? How does this law relate to energy conservation.
Many electric motors, especially large ones, have a starting resistance. Clearly explain why this is needed.
A student set up an experiment similar to that in the diagram below. Explain the student's observations.
Aluminium disk spins freely on its axle
Solid disk stops spinning when magnetic field brought close to disk A disk with slits continues to spin for much
longer than a solid disk in the presence of a magnetic field
Generators use the principle of _____ induction to convert _____ energy into energy.
AC generators have four essential features. These are:
______________ and _____________ _
DC generators also have the four essential features of AC generators but they also have a . This is used to convert into ____ _
Generators work by moving a conducting coil to a magnetic field. As the coil rotates, the magnetic through the coil varies and so a/an is induced between the ends of the coil.
Maximum emf is produced when the coil passes through the horizontal plane. True or false? ___ _
In what direction is the emf induced in the generator (Lenz's law)? ____ _
Real generators differ from the simplified idealised models discussed in class. Three ways in which they differ are:
___________________________________ and
The biggest loss of energy from where it is generated in the 'power station' to the consumer occurs in the where some of the electrical energy is converted into ____ _
Electricity has impacted on society in a number of ways including:
_________________________________ and
High voltage power lines are said to be associated with increased risk of certain ____ . There is currently evidence about these alleged health risks.
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Electric generators use the principle of electromagnetic induction to convert mechanical energy into electrical energy (the reverse of electric motors). The mechanical energy can be supplied by steam derived from water heated by the combustion of fossil fuels or the heat from nuclear reactors, by the kinetic energy of falling water (hydroelectricity) or wind generators.
Generators consist of an armature, field structure, slip rings and brushes as in the diagram.
In addition to the structures in 2 above, DC generators also have a commutator whose role is to convert AC into DC.
Generators work by moving a coil relative to a magnetic field. Consider the simplified diagram of an AC generator. As the coil is made to rotate, the magnetic flux through the coil varies, from a minimum when the coil is parallel to the field, to a maximum when the coil is
Carbon brushes held in place by springs
Field magnets
AC generator
perpendicular to the field. As a result, an emf is induced between the ends of the coil and current can flow in an external circuit.
Faraday's law says that the emf is proportional to the rate of change of magnetic flux through the circuit. Hence the emf varies from a maximum as it passes through the horizontal plane (the rate of change is greatest here) to a minimum as it passes through the vertical plane.
In agreement with Lenz's law, the emf is induced in such a direction that its associated current flows in a direction so that its magnetic field opposes the cause of the induced emf.
Time
2 3 4 5
AC generator output
Real generators differ from the simplified model used above. In general, real generators use electromagnets to produce the magnetic field rather than permanent
magnets; have hundreds of coils wound around a soft iron core; have the armature as the stator (the non-moving part) in AC generators - it is the rotor in DC generators; have three pairs of electromagnets place at 1200 to each other (producing three-phase power).
Some energy is lost in transmission from the power station to where it is used. This can occur because of friction in the rotor bearings; heat generated by currents in the transmission cables and energy losses in the generator's iron core.
Electricity has profoundly affected society. The discovery of how to generate large amounts of electricity and transport it to distant sites led to electricity becoming the primary source of industrial and domestic energy. This exacerbated some of the problems of the industrial revolution - the shift of the population from the country to city slums, longer working hours ... as well as the associated current environmental issues of global warming and acid rain.
Controversy exists about the alleged harmful affects of living close to power lines. A number of scientific investigations have been done on the relationship between the occurrence of certain cancers and the proximity of living near high voltage power lines. The results are conflicting or inconclusive: some investigations show a statistically valid association; others do not. The jury is still out.
CHECKLIST - Can you: 1. Identify the main components of a generator? 2. Compare a generator with a motor? 3. Describe the principle of operation of AC and DC generators? 4. Compare the advantages and disadvantages of AC and DC generators? 5. Explain how energy is lost as it is transmitted from the generator to the consumer? 6. Describe the effect of electricity on society and the environment?
The device that changes the direction of the current in a DC generator is the: armature brush commutator slip rings
In a simple AC generator, a coil of wire is placed between the poles of two magnets and is rotated in an anticlockwise direction as shown. Sketch the expected output on the axes provided at the positions indicated by the numbers 1-5. Repeat on the second set of axes for a DC generator.
~ 0
~ 0
~ 5;:> 5;:> 2 3 4 5
OJ OJ OJ OJ
.l!l .l!l ~ ~
Time
The first continuous current-generating device was invented by Michael Faraday and was called Faraday's disk dynamo. It consisted of a copper disk that could be rotated between the poles of a strong magnet. Copper brushes carried current away. Briefly explain how this works.
Clearly describe the effects of the development of AC and DC generators on society and the environment.
Copper brushes
Time
Transformers are used to electrical energy from one circuit to another. They can also be used to change the AC ___ _
Transformers consist of three essential features, a _____ coil, a _____ coil and a soft core.
_____ voltages in the coil induce changing voltages in the ____ _ coil by the process of mutual induction.
Transformers operate on only.
In a step-down transformer: the current in the secondary is less than the current in the primary the voltage in the secondary is greater than the voltage in the primary the voltage in the secondary is less than the voltage in the primary.
In a step-up transformer there are more coils in the primary than in the secondary. True or false? ____ _
In an ideal transformer, the power in the secondary is same/different from the power in the secondary? ____ _
In a step-up transformer, compared to the secondary, the voltage and current in the primary are respectively:
bigger and bigger bigger and smaller smaller and bigger
A transformer has a primary of 1000 turns and is used to step-up the voltage from 12 V to 240 V.
How many turns are needed in the secondary? (Assume 100% efficiency.) What current flows in the primary if the secondary is operating at 12 W?
To minimise energy losses in transmission, electricity is transmitted at voltages as high as V.
Transformers in electricity _____ are used to reduce the voltages to suitable amounts for homes and industry.
Many household appliances contain ___ _
Energy losses due to eddy currents are minimised in transformers by having the soft iron core ___ _
Transformers and generators have had a ____ impact on our lives.
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Transformers are devices for transferring electrical energy from one circuit to another. They also allow AC voltages to be easily changed in magnitude.
Transformers consist of two coils the primary and the secondary both of which are wrapped around the same soft iron core. The primary coil has alternating voltages supplied to it. The secondary has alternating voltages induced in it.
Changing AC voltages in the primary sets up a changing magnetic flux in the soft iron core. This sets up a changing magnetic field in the secondary coil and so an emfis induced in it. The process is called mutual induction.
Transformers operate on AC only and not DC. This is because a changing magnetic field is required for electromagnetic induction to occur.
A step-up transformer increases the voltage in the secondary coil compared to the primary coil. Conversely, in a step-down transformer the secondary voltage is less than the primary voltage.
A step-up transformer has more coils in the secondary than in the primary. In a step-down transformer, the secondary has fewer coils than the primary.
The conservation of energy necessitates that in an ideal transformer, the power in the primary circuit is equal to the power in the secondary circuit. Since P = VI it follows that as voltage increases, the current decreases.
It follows that in a step-up transformer, the voltage in the secondary is larger than the voltage in the primary but the current in the secondary is less than the current in the primary.
In an ideal transformer (100% efficient) the voltage, current and number of turns
V n I (coils) are related by vP = L = -IS
5 ns P
Power is transmitted at extremely high voltages, as high as 500 kV (500 000 V). This is done to reduce the current and so lessen the energy losses in the transmission lines where the heating effect in the wires is proportional to the square of the current.
Transformers in sub-stations are used to change the voltage (and current) to values suitable for use in industry and households by stepping the voltage down. This is generally to 240 V for household use and 415 V for industriallcommercial use.
Many home electrical appliances such as TVs and computers require voltages other than the 240 V supplied to homes. Transformers are able to change the voltage to the required amount.
Transformers limit eddy currents in their core by having the core made of individual sheets (laminates) electrically insulated from each other. This lessens energy losses due to heating of the iron core.
The invention of transformers (along with generators) meant that electricity could be easily distributed around the country and so electricity became the energy source of the industrialised world. This has had significant impact on the way we live. No longer are we restricted to daylight hours for work. We can now communicate almost instantaneously via radio, TV, mobile phones (the batteries of which require charging), etc. Greenhouse gas emission from fossil-burning fuels is a significant environmental issue. Imagine your life without electricity.
CHECKLIST - Can you: 1. Explain the use and principle of operation of transformers? 2. Compare step-up and step-down transformers?
3. Solve problems using V p =:2.e.. = ~ Vs ns Ip
4. Relate voltage and current changes to energy conservation? 5. Explain the role of transformers in electricity sub-stations and in the home? 6. Describe how transformers have impacted on society?
A transformer can be used: to increase voltage to decrease current both a and b to increase power.
A schematic diagram of an electric transformer is shown.
Primary coil
What is the purpose of transformers?
Secondary coil
Output voltage
Clearly explain how a transformer works, describing the role of each of the labelled components. If the primary has 1000 turns and the secondary has 250 turns, what is the secondary voltage if the primary voltage is 240 V? (Assume 100% efficiency.)
Eddy currents can be a problem in power generation. Discuss how these eddy currents arise and how they can be minimised to lessen their impact.
The transfer of electrical energy from electric power stations to the consumer is not 100% efficient. Briefly discuss the energy losses involved and how they are kept as low as possible.
AC electric motors have a _____ and a ____ _
AC motors, unlike DC motors do not require a ____ _
The most common type of AC motor is the _____ motor.
These motors work on the principle that a _____ magnetic field will exert a _____ on a stationary coil.
A rotating magnetic field can be relatively easily produced by using ___ _
A field like that above will _____ a current in the coil. Interaction of the two fields results in the coil being around.
AC induction motors are widely used because of their ________ design, relatively cost and their ______ _
The electric motor used in small appliances such as food processors and electric power saws is most likely to be:
a single-phase AC induction motor a three-phase AC induction motor a DC motor an AC synchronous motor.
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AC electric motors have two essential features - a rotor (the moving part) and the stator (the stationary part). Some also have slip rings to bring electricity to and from the motor.
AC electric motors have the advantage over DC motors in that they do not require a commutator (the AC automatically reverses 50 times per second). Commutators have problems associated with sparking, ozone production from the sparking and energy loss in the brushes. In addition there are problems with the wearing of the brushes.
The most common type of AC motor is the induction motor.
AC induction motors work on the principle that a rotating magnetic field will exert a torque on a stationary coil.
AC can relatively easily produce a rotating magnetic field.
AC induction motors work by having the stator produce a rotating magnetic field. This induces (hence induction motor) an electric current in the rotor by the process of electromagnetic induction. This current produces a second magnetic field. The two magnetic fields interact with the rotating field dragging the rotor around.
AC induction motors are cheap, efficient and simple to manufacture which accounts for their wide use. In particular they are used for low power « 1 kW) applications in homes.
95% of all electric motors are single-phase induction motors. These represent the majority of motors in the home. Industry tends to use three-phase induction motors since they can have larger power ratings.
CHECKLIST - Can you: 1. Describe the main features of an AC electric motor? 2. Describe the principle of operation of AC induction motors? 3. Relate the power rating of AC motors to their uses? 4. Explain the advantages of AC induction motors?
In an AC induction motor: current is induced in the rotor current is induced the stator current is supplied to the rotor from an external source a commutator converts AC to DC.
AC induction motors have the advantage over DC motors that: they don't require a commutator they are simple to design they are relatively cheap all of the above.
Many power tools and appliances used in the home have relatively low power -0.5-1 kW. Explain why these are most likely AC induction motors.
Briefly describe the principle of operation of an AC induction motor.
The German Geissler invented a pump efficient enough to reduce the pressure in a glass tube to a small fraction of normal air pressure. By placing metal ____ in these tubes it was possible to get to flow through the tubes.
As the pressure is reduced in these tubes, different patterns were produced that depended on the gas pressure.
At a low pressure of -0.01 kPa a green glow appears in the end of the glass tube opposite the negative electrode, the ___ _
This glow was found by Crookes to be caused by emanating from the negative electrode.
Charged particles can be affected by: electric fields magnetic fields both electric and magnetic fields.
Various cathode ray tubes and certain properties of cathode rays are shown. Draw a line that correctly links the tube with the property.
Cathode ray tube Property Maltese cross rays carry energy and momentum magnet brought near rays travel in straight lines fluorescent screen paddle wheel i rays are deflected by magnetic fields
The nature of cathode rays, ____ or , was long debated.
A parallel plate capacitor is a useful device because it provides a ____ electric field, the intensity of which is calculated from the equation ___ _
A charge of 3.2 x 10-19 C moves at right angles to a magnetic field of 0.1 T at a speed of 2.0 x 107 m.s-1. What is the magnitude of the force acting on the charge?
J.J. Thomson successfully measured the ____ to -,-___ ratio for cathode rays.
A cathode ray tube has three main components _____ _ _ __ --,-__ and
Cathode ray tubes are found in ___ _ ____ and ___ _
The cathode ray ____ is a useful experimental measuring device.
The ____ nature of electrons is used in electron ___ _
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Plucker showed that as the pressure is reduced in the discharge tube, a series of changes progressively takes place. Gas discharge tubes produce different striation patterns determined by the gas pressure.
Crookes' dark space
Negative glow
Positive column
Faraday's dark space
Discharge tube
Anode glow
+
At a pressure of -0.01 kPa a green glow appears in the glass tube behind the anode and opposite the negative electrode (cathode).
In 1875 Crookes deduced that the green glow was caused by cathode rays that travelled from the cathode.
Cathode ray tubes allow the manipulation of moving charged particles by electric and magnetic fields.
Cathode ray tubes come in a range of types including Maltese cross and a paddle wheel. From these tubes we can deduce various properties of the cathode rays (see diagrams). The Maltese cross tube shows they travel in straight lines; the tubes with a fluorescent screen show they are deflected by magnetic and electric fields and the paddle wheel tube shows they carry energy and momentum.
Maltese cross
Different types of cathode ray tubes
The nature of cathode rays - whether they are a wave or a particle - was long debated. In 1887 J.J. Thomson determined their nature as being particles. Some years later his son G.P. Thomson showed cathode rays to be waves!
Surrounding any charge is an electric field. Of special interest is that a uniform electric field exists between two parallel plates, the strength of which is found from E = V/d.
A charge moving in a magnetic field experiences a force given by F = qvB sin e. If the charge enters the field at 90° it moves in the arc of a circle.
In 1897, Thomson successfully measured the charge to mass ratio (q/m) for cathode rays. He used apparatus similar to that in the diagram. By suitably arranging the strength of the electric and magnetic fields it was possible to derive an expression for q/m. Thomson found that all cathode rays had the same q/m ratio equal to 1.76 x 1011 C.kg-1•
gun
Collimator
+ Coil to produce magnetic field
Site of evacuation
/ Fluorescent screen
A cathode ray tube (CRT) has an electron gun, a deflecting
Thomson's apparatus to measure qlm ratio
Accelerating anodes
Spot of light
system and a fluorescent screen. The electron gun provides a beam of electrons, the deflecting system controls the electron beam and is made of two pairs of parallel plate capacitors in the x- and Y- planes respectively. The fluorescent screen indicates the position
V-plates X-plates
of the electron beam, giving off light Filament
when impacted by an electron.
CRTs are used in a wide range of devices including cathode ray oscilloscopes, electron microscopes and television sets.
+
Grid
Electron gun
Deflection system
A cathode ray tube
Fluorescent screen
The cathode ray oscilloscope is used to 'view' electrical signals or waveforms. Its invention has had a significant impact on experimental physics.
Electron microscopes use the wave nature of electrons to magnify tiny objects. Magnets focus the electrons.
CHECKLIST - Can you: 1. Explain how cathode rays tubes are used to control charged particles? 2. Explain the cause of the uncertainty in the nature of cathode rays? 3. Calculate the uniform electric field of a parallel plate capacitor using E = Vld? 4. Correctly use the equation F = qvB sin e? 5. Describe Thomson's experiment to determine the charge to mass ratio for electrons? 6. Explain the role of the various components of a cathode ray tube? 7. Outline some uses of cathode ray tubes? 8. Explain the principle of operation of photocopiers and lightning rods?
The diagram is a representation of apparatus commonly used in school science laboratories to investigate the effect of pressure on the electric discharge through a gas. The pressure in the leftmost tube is -1 kPa and that on the right is -0.01 kPa.
What is observed in the leftmost tube when connected to the high voltage supply? What is observed in the rightmost tube when connected to the high voltage supply?
Cathode /
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- +
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Two pieces of apparatus illustrated below are used to demonstrate various properties of cathode rays.
Maltese cross !
Paddle wheel
Tube 1 Tube 2
What property is demonstrated in tube 1? Explain your reasoning. What property is demonstrated in tube 2? Explain your reasoning.
In 1897 J.J. Thomson used apparatus similar to that shown in the diagram.
Site of evacuation
What was the purpose of the ---Electrodes
experiment? Explain (using equations where possible) the role of the electric and magnetic fields.
Photocopiers and lightning rods both use the electrical discharge from a sharp point
Electron gun
in their operation. Briefly describe how this is used in a photocopier or lightning rod.
,
+ Coil to produce magnetic field
Fluorescent screen
Hertz measured the speed of radio waves and found it to be the same as the speed of light. True or false? ___ _
While investigating the generation of radio waves, Hertz discovered the ____ _ effect.
Electromagnetic waves are produced by: electrons orbiting the nucleus charges moving with constant speed in conductors charges oscillating in conductors.
A black body is a perfect ____ and a perfect ____ of radiation.
The black body radiation curves could/could not be explained by classical physics?
Planck proposed that the emission and absorption of energy by a black body is _____ . This means it comes in amounts.
This photoelectric effect is the emission of _____ from materials under suitable conditions.
When light is shone on a particular metal no electrons are emitted. This is probably because:
the light frequency is too low the light intensity is too low the time the light was shining on the metal was too short.
In his analysis of the photoelectric effect, Einstein proposed that light energy is concentrated in whose energy is given by ____ _
The photoelectric effect is used in _____ , solar _____ and
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In 1887 Hertz first demonstrated the production of electromagnetic waves (he actually produced what we now refer to as radio waves). He successfully measured the speed of these waves and found them to be travelling at the same speed as light. He thus deduced that light is a transverse electromagnetic wave.
Hertz discovered the photoelectric effect while investigating the generation of electromagnetic (radio) waves but failed to investigate it further.
Electromagnetic waves are produced by charges oscillating in conductors (for example, radio antennae). The oscillation of electrons can be produced by connecting the aerial to an alternating current source.
Black bodies are perfect emitters and absorbers of radiation.
Black body radiation curves, which relate the maximum frequency of emission to the temperature of the black body, are unable to be explained by classical physics (the physics of Newton and Maxwell).
In an attempt to explain the black body radiation curves, Max Planck proposed in 1900 that emission and absorption of electromagnetic radiation for a black body is quantised. This means that the energy is not continuous but is in discrete amounts. These amounts are
200 400 600 800 1000 A(nm)
Black body radiation curves
given by E = hf where E is energy, h is Planck's constant (6.626 x 10-34 J.s) and f is the frequency of the light.
The photoelectric effect is the emission of electrons from substances when irradiated with light (that is, electromagnetic radiation).
There was major conflict between the results of experiments on the photoelectric effect and classical physics. For example, the experimental results indicated that emission was frequency dependent, that is, below a certain frequency no electrons were emitted regardless of the light intensity. Classical physics predicted no frequency dependence.
In 1905 Einstein explained the photoelectric effect and in doing so proved the particle nature of light. He proposed that energy is concentrated in 'bundles' called photons with energy given by the Planck relationship E = hf.
The photoelectric effect is put to use in: breathalysers - a device used by police to measure the blood alcohol content of drivers suspected of driving 'under the influence'; colour changes initiated by the alcohol are measured by photosensitive devices in the analyser solar cells - these employ the semiconductor silicon and are used to convert solar energy directly into electrical energy photocells - photoelectric cells in which the electrons of an electric current are produced by the photoelectric effect; they are used in devices such as electric 'eyes', radiation detectors and light meters.
CHECKLIST - Can you: 1. Describe Hertz's experiments on electromagnetic radiation and his discovery of the photoelectric
effect? 2. Describe the generation of radio waves? 3. Discuss Planck's hypothesis on the quantisation of energy? 4. Describe Einstein's contribution to our understanding of the photoelectric effect? 5. Solve problems using E = hf and c = fA
Heinrich Hertz is credited with discovering the photoelectric effect. What was Hertz investigating when he made the discovery? What did he do that led to the discovery of the photoelectric effect?
Briefly describe how electromagnetic waves are generated.
Planck proposed the quantisation of energy to help explain: the black body radiation curves the photoelectric effect the generation of electromagnetic waves su percond uctivity.
A graph of the maximum kinetic energy of photoelectrons as a function of wavelength for a metal X is shown.
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:.s2 x ro ~
What is the significance of the point where the line cuts the frequency axis?
Light of frequency 1.6 x 1015 Hz is shone on metal X. Describe what happens.
The de Broglie model of the atom pictures the electrons as: moving in definite orbits around the nucleus moving as matter waves around the nucleus.
When two or more atoms are brought near to each other, the energy levels ___ _
The band model of matter has two bands, the ____ band and the ___ _ band.
In metals, the two bands ___ _
If an electron jumps from the lower or ____ band to the higher or ___ _ band, it leaves a behind.
Electric current is carried by both ____ and ___ _
Conductors have more/less free electrons than semiconductors? ___ _
When a Group III or Group V atom is substituted for an atom of germanium or silicon, we say the material has been ___ _
____ a semiconductor alters its electrical properties.
In p-type semiconductors, are the majority carriers. In n-type semiconductors, ____ are the majority carriers.
____ was the first semiconductor commercially used because it was easily purified.
____ is now the preferred semiconductor because of its ___ _
When a metal is heated: electrons are emitted by photoemission electrons are emitted by thermionic emission holes are emitted by thermionic emission.
Solid state devices can be made bigger/smaller than thermionic devices? ___ _
____ have had a major impact on society.
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de Broglie's model of the atom pictures atoms as having the electrons moving as matter waves around the nucleus, rather than as discrete particles proposed in the Bohr model of the atom.
Isolated atoms have discrete energy levels. When two or more atoms come together, the energy levels split. As a result, electrons can be shared between atoms. For a finite amount of matter containing billions of atoms, the individual energy levels form a continuum resulting in energy bands.
Isolated atom Two close atoms
Formation of energy bands
~~~ Conduction band
Forbidden energy gap
~~~ Valence band
Energy bands
The energy bands are the valence band and the conduction band, separated by the forbidden energy gap.
Conductors, semiconductors and insulators differ in their band structure as shown in the diagram on the right.
In some circumstances it is possible for an electron to jump from the valence band to the conduction band leaving a (positive) hole behind. Holes represent the absence of electrons in a nearly full band.
Conductor
Forbidden energy gap
Semiconductor
Band structure
Insulator
Both holes (positive charge) and electrons (negative charge) can carry electric current.
Conductors, semiconductors and insulators differ in the number of free electrons that can move between atoms. Conductors have many, semiconductors have a few and insulators have almost no free electrons.
When a Group III or Group V atom is substituted for a Group IV atom of germanium or silicon we say the material has been doped.
Doping a semiconductor alters its electrical properties. The electrical conduction can be improved significantly because it provides additional charge carriers.
In p-type semiconductors, a Group III atom is substituted so holes are the majority carriers (and electrons are the minority carriers).
p-type semiconductor
In n-type semiconductors, a Group V atom is substituted and so electrons are the majority carriers (and holes are the minority carriers).
Pentavalent atom
···8
n-type semiconductor
Germanium was the first semiconductor material because of its relative ease of purification.
Silicon is now the preferred semiconductor material. It is more abundant and hence cheaper, and it retains its semi-conducting properties at higher temperatures than germanium.
Thermionic emission is the spontaneous emission of electrons from solids when heated to high temperatures. Thermionic valves rely on this effect for their operation. They include the diode, triode and pentode, the latter two being used as amplifiers in old-style (and bulky) radios, televisions, etc.
Solid-state devices have all but replaced thermionic devices. This is because solid state devices can be made much smaller (miniaturised), use less power and react faster.
Transistors have had a significant impact on society. They have led to the computer driven 'information age' that has revolutionised communication.
CHECKLIST - Can you: 1. Describe de Broglie's model of the atom? 2. Describe the band structure of conductors, semiconductors and insulators? 3. Explain the concept of a hole? 4. Explain how doping can affect the conductivity of a semiconductor? 5. Describe the difference between p- and n- type semiconductors? 6. Explain why germanium was the original semiconductor of choice but has now been replaced by
silicon? 7. Compare solid state devices with thermionic devices? 8. Discuss the impact of transistors on society?
Following is a diagrammatic representation of energy bands in conductors, semiconductors and insulators.
Forbidden energy gap
Conductor Semiconductor Insulator
Why does matter form energy bands? What is the significance of the absence of a forbidden energy gap in metals?
Germanium was originally the preferred semiconductor material. It has since been superseded by silicon. Explain why germanium was previously used but now silicon is preferred.
Doping can markedly change the conductivity of semiconductors. What is meant by doping? Explain how doping silicon with a Group III element produces holes as the majority carriers.
Thermionic devices have all but been replaced by solid state devices. What are thermionic devices? What are solid state devices? Give three reasons why solid state devices have superseded thermionic devices.
The father and son team of the Braggs investigated the structure of matter by bombarding it with:
electrons neutrons light X-rays.
Metals were shown by the Braggs to have a __________ structure.
Metals tend to have ____ _ _____ or _____ electrons in their outer shell.
The current model of a metal pictures it as having: a lattice of positive ions surrounded by a sea of neutrons a lattice of positive ions surrounded by a sea of electrons a lattice of electrons surrounded by a sea of protons.
Electricity conduction in metals results from the _____ of a large number of _____ through the lattice.
The drift velocity depends on ____ _ _____ and ____ _
Heat is generated during conduction because the lattice _____ the electrons.
As temperature increases, _____ to conduction increases.
_____ allow electrons to flow unimpeded.
Superconductors have zero resistance: at all temperatures below a certain temperature above a certain temperature
A magnet floating above a superconductor material illustrates the effect.
Electrons pass unimpeded through a superconductor in pairs.
One current use of superconductivity is in magnetic _____ imaging.
_____ trains use magnetic levitation.
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Sir William Bragg and his son Sir Lawrence Bragg investigated the internal structure of crystals by using X-rays to form diffraction patterns. They were able to show that crystals had atoms arranged in a regular pattern and were also able to determine the interatomic spacing. X-ray crystallography is an important investigative technique into the structure of materials.
By using X-ray crystallography scientists were able to show that metals possess a crystal lattice structure.
Metals tend to have one, two or three electrons in their outer shell. These electrons are only loosely held by the atoms and hence are able to move.
The electron sea model of metals pictures them as having a lattice of positive ions surrounded by a 'sea' of electrons.
Electricity conduction in metals results from the drift of a large number of electrons through the lattice. This drift results when a potential difference is applied between the ends of the metal conductor and is superimposed on the otherwise random wanderings of the electrons.
The drift velocity of the electrons in a conductor is related to the density of electrons, the cross-sectional area of the conductor and the charge on the carriers. For example, the larger the area, the greater the drift velocity as there are more gaps for the electrons to move through.
ion electron
Electron sea model of a metal
drift direction
U U low
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Electron drift in conductors
Heat is generated as the lattice impedes the electrons. In fact it is imperfections in the lattice and the presence of impurity atoms that restricts the movement. This restriction of the flow of electrons is what gives a conductor its resistance.
The higher the temperature of a metal conductor, the higher the resistance. This is because impurity ions in the lattice vibrate more and so the probability of hitting the conduction electrons increases.
It follows that if resistance increases with temperature then as temperature decreases, so too should the resistance. A class of material exists - superconductors that allow electrons to flow unimpeded. The resistance is effectively zero.
The temperature at which material become superconducting is called the transition temperature. This temperature has steadily risen from 4.2 K for mercury (the first material to be found to be a superconductor) to current high-temperature superconductors with a transition temperature as high as 134 K.
Superconductors have the ability to prevent penetration of a magnetic field. This is called the Meissner effect and is illustrated by a magnet floating above a superconductor. It is also used in Maglev trains.
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The BCS model of superconductivity is a quantum-mechanical effect where two electrons pair up - a Cooper pair - and move unimpeded by the lattice. As the temperature increases above the transition temperature, the Cooper pairs break apart and the superconductivity ceases.
Lattice distortion
~
Superconductors have many advantages but are still limited in their use. Cooper pairs form when two electrons become 'locked Current uses include: together' and travel through the lattice.
Magnetic resonance imaging (MRI) Cooper pairs where they produce intense magnetic fields for use in medical diagnosis SQUIDS (superconducting quantum interference devices) that can measure minute differences in the Earth's magnetic field Maglev trains that rely on the levitation, achievable with powerful magnets to reduce friction, resulting in high speed travel.
Proposed uses include: in electricity transmission where eliminating the resistance of transmission (power) lines would save enormous amounts of energy in generators and motors where the magnetic fields could be very intense even for small magnets. electronic switches using the Josephson effect in computers for high speed processing.
Experimental Maglev trains exist in Germany and Japan. Both rely on magnetic levitation to lift the train's wheels off the track so reducing the friction. Linear motors give the train its propulsion.
CHECKLIST - Can you: 1. Describe x-ray crystallography as first done by the Braggs? 2. Describe the crystal structure of metals? 3. Describe the factors affecting drift velocity? 4. Explain the BCS theory of superconductivity whereby superconductors allow free movement of
electrons? 5. Identify current and proposed uses of superconductors?
Materials become superconducting: above a critical frequency below a critical frequency above a critical temperature below a critical temperature.
The crystalline structure of certain materials was first demonstrated by: X-ray diffraction neutron diffraction the photoelectric effect the Meissner effect.
The current uses of superconductors is limited because: they are too expensive to make the materials used are extremely rare there is no need for them they require extremely low temperatures to operate.
One of the current uses of superconductors is in magnetic resonance imaging (MRI) machines. These are medical diagnostic machines used to provide extremely good 'pictures' of a patient's internal tissues/organs. Explain what the superconductor is used for in this device.
The BCS theory of superconductors is a quantum-mechanical explanation of superconductivity. Briefly describe the theory.
Ultrasound is sound with frequencies greater than _____ Hz.
Special devices called _____ produce ultrasound. These convert one form of energy into another.
_____ crystals are used to produce ultrasound by connecting them to suitable AC frequencies.
Muscle has a density of 1.07 x 103 kg.m-3 and sound travels through it at 1540 m.s-1. What is the acoustic impedance of muscle?
Three different tissues have the acoustic impedances shown in the table. The greatest reflection will be between which two tissues? _____ and ____ _
_____ is the use of ultrasound in medical applications.
Tissue
bone
fat
soft tissue
Acoustic impedance (x 106 kg.m-2.s-1)
7.8
1.38
1.70
Ultrasound imaging is a non- _____ method of 'seeing' into the human body.
Ultrasound imaging modes (modalities) include: ___ _ _____ and
In scans a single transducer scans along a _____ in the body. The resulting echoes are plotted as a of time.
In scans an array of transducers scans a _____ in the body. The resulting echoes are plotted as varying of the signal.
In a scan a fan-shaped image is formed. This is familiar to us as a scan of a _____ in a mother's womb.
The Doppler effect is the change in frequency when there is ____ _ motion between a source of sound and an observer.
Doppler _____ is commonly used to examine blood flow and heart functioning.
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Ultrasound is sound (that is, a longitudinal mechanical wave) with frequencies greater than 20,000 Hz (20 kHz) which is the upper limit of human hearing.
Special transducers (devices that convert one form of energy into another) produce ultrasound.
The most common ultrasound transducers are piezoelectric crystals such as lead zirconate titanate. These convert an oscillating potential difference into mechanical oscillations and vice versa. By applying appropriate AC frequencies to a suitable crystal, ultrasound can be produced as the crystal oscillates at the AC frequency.
The acoustic impedance (Z) is a measure of how easy it is to transmit sound through a medium. It depends on the speed of the wave in the medium (v) and the density (p) of the medium Z = pv
Different media have different acoustic impedances and so reflect sound differently (see table). The greater the difference in acoustic impedance between two materials, the greater will be the reflection from the interface of those two materials.
Ultrasonography is the use of ultrasound in medical (and industrial) applications. It can be active (for example, breaking up gall stones) or passive (for example in scanning).
Material
air fat water brain blood kidney liver muscle lens of eye bone (average) skull-bone
Z (x 106 kg.m-2.s-1)
0.0004 1.38 1.54 1.68 1.61 1.62 1.65 1.70 1.84 6.5 7.8
Ultrasound imaging is a non-invasive method (no surgical procedure is required) that uses ultrasound to 'see inside' the human body. A transducer is held against the skin with a coupling gel and an ultrasound pulse is emitted. The pulse reflects offthe different tissue interfaces and the internal structures can be mapped.
Imaging modes include A-, B-, sector and phase scans and each has its advantages.
In A-scans (amplitude scans) a single transducer scans along a line in the body and the reflected echoes are plotted as a function of time. Rarely used, this scan does have advantages for detailed measurements ofthe eye. It works much like sonar as a 'depth finder'.
In B-scans (brightness scans) an array of transducers scans a plane in the body. The brightness of the signals caused by the echoes is determined by the amount of reflection.
8-scan
Organ or other structure
• 0 Dots have different brightness related to signal strength. The greater the signal strength the brighter (whiter) the dot. The weaker the strength, the darker the dot.
A- and 8-scans
Sector scan
In a sector scan the beam is made to sweep over the required part of the patient and a fan-shaped scan is produced. The results are shown on a television monitor as a 'real time' image. This is the common scan seen of a foetus in the womb as in the scan above.
The Doppler effect is the apparent change in frequency when there is relative motion between a source of sound and the observer. When the source and observer approach each other the frequency increases; when they are moving apart, the frequency decreases.
Doppler echocardiography is commonly used to examine blood flow and the condition of the heart. If the blood flows towards the transducer the frequency increases. Similarly if it flows away from the transducer, the frequency decreases. By using 'false colour' an easily identified picture of the blood flow can be made in real time.
CHECKLIST - Can you: 1. Describe what ultrasound is and how it is produced by piezoelectric transducers? 2. Define acoustic impedance and calculate its value for a range of materials? 3. Explain how ultrasound and different acoustic impedances of materials are used in ultrasound scans?
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5. Describe the different scan types: A-, 8- and sector scans and explain where they are best used? 6. Describe the Doppler effect and how it can be used to monitor blood flow through the heart?
PZT (lead zirconate titanate) is a piezoelectric crystal commonly used as a transducer to generate ultrasound.
What is a piezoelectric crystal? How is this crystal used to produce ultrasound?
The frequencies commonly used in medical ultrasound lie in the range 1 MHz to 15 MHz. Suggest why these frequencies are suitable for medical imaging.
The speed of sound in blood is 1570 m.s-1 and blood has an acoustic impedance of 1.61 x 106 kg.m,2.s-1
What is meant by the acoustic impedance of blood? What is the density of blood?
The following table gives the acoustic impedances of some different media. Use this to explain why ultrasound is not good at imaging the lungs (which consist essentially of sacs of air covered by muscle and surrounded by the rib cage).
Tissue Acoustic: impedance
(x 106 kg.m-2 .s-')
air 0.0004
bone 7.8
fat 1.38
muscle 1.70
Using the table above, calculate the ratio of the reflected intensity of sound to the intensity of the incident sound from a fat/muscle interface.
X-rays are high frequency _____ waves produced when ____ are rapidly decelerated.
X-ray tubes have three essential features: ______ _ _______ and
It is more difficult for hard X-rays to penetrate matter than soft X-rays. True or false?
The higher the density of a material, the more/less X-ray energy it absorbs? ___ _
A standard X-ray image or is made by passing X-rays through a patient and allowing the transmitted rays to fall on a photographic film. An image forms as the result of shades of black/white/grey on the film.
Conventional X-rays are good/poor at distinguishing between different soft tissues.
Computerised tomography (CAT) uses X-rays and ____ to make detailed images of a patient's internal organs.
CAT is better/worse at soft tissue differentiation than an ordinary X-ray? ___ _
In a CAT scan the patient is placed inside a circular scanner called a . X-rays are fired at different through the patient enabling a 'slice' of the patient to be displayed on a ___ _
CAT is morelless sensitive than conventional X-rays. ____ _
A tube used to look inside the body is called a/an ___ _
An image in an optic fibre ____ is transmitted by a ____ bundle.
Two important uses of the device in 12 above are _____ internal organs and obtaining samples for investigation.
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X-rays are extremely high frequency electromagnetic waves. They are produced in an evacuated chamber by bombarding a tungsten target with electrons.
X-ray tubes consist of a negative cathode, a high accelerating potential difference (25 kV - 250 kV) and a positive anode with a high temperature-resistant tungsten target. Electrons accelerated from the cathode strike the target and are rapidly decelerated. Their kinetic energy is converted into X-rays (1 %) and heat (99%).
Tungsten target
Lead shielding
Vacuum
Cathode filament x- rays +
Very high potential difference
The wavelength (and hence frequency) of the X-rays can be controlled by the accelerating potential. Hard X-rays have short wavelengths (-0.01 nm); soft X-
Modern X-ray tube
rays have longer wavelengths (-1 nm). Soft X-rays have less penetration than hard X-rays.
X-rays can be used to 'see inside' the human body. Different materials such as bone and muscle absorb X-rays differently. The higher the density, the greater the absorption.
A radiograph is made by passing X-rays through the patient and allowing the transmitted X-rays to fall on a photographic film. The different shadows from clear (high absorption) to opaque (minimal absorption) produce the image as in the radiograph.
Conventional radiographs cannot distinguish between soft tissues very readily.
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Computerised axial tomography (CAT or CT) is a method that uses X-rays and computers to make a detailed picture of the inside of the human body. Radiograph
CAT improves the clarity of soft tissue differentiation. In a simple radiograph there are 32 shades of grey; in CT there are 256 shades of grey.
To produce an image the patient lies on·a table that can be moved into a circular scanner or gantry as in the photograph. X-rays from the gantry are fired through the patient and are detected by special detectors. By firing the X-rays from different angles a 2D 'slice' of the patient can be built up. This is displayed on a television monitor. A series of slices can also be produced to 'reconstruct' an entire organ in 3D.
Patient having a CAT scan
CAT is more sensitive than conventional X-rays and is ideal for detecting cancerous tumours, blood vessel blockages, fractures etc
An endoscope is a tube that uses optical fibres to look inside the body. The fibre optic endoscope uses tens of thousands of optic fibres that use the principle of total internal reflection to allow the endoscopist to literally 'see round corners'.
A coherent bundle is made by placing the fibres in the same relative position at both ends of the cable. This allows an image to be transmitted without distortion.
Endoscopes assist in observing internal organs and in obtaining tissue samples for biopsy. In the latter, miniature surgical instruments in the endoscope casing allow tiny samples to be removed for analysis.
CHECKLIST - Can you: 1. Describe the nature and production of X-rays? 2. Distinguish between 'hard' and 'soft' X-rays? 3. Describe how a CAT scan is produced? 4. Explain the advantages of CAT over simple X-rays and ultrasound? 5. Explain how an endoscope works including incoherent and coherent bundles of fibres? 6. Explain the uses of an endoscope?
Wilhelm Roentgen first discovered X-rays in 1895. What are X-rays? How are they produced? What is the difference between 'hard' and 'soft' X-rays?
To the right is a radiograph of a compound fracture of the shaft of the humerus (the upper arm bone). Briefly describe how such a radiograph can be produced.
Below is a CT scan of a cancer patient's liver showing secondary malignant cancers (metastases) as dark areas.
What is a CT scan (also known as a CAT scan)? Explain how such a scan can be made. What is the advantage of CAT over conventional X-rays like the radiograph in Question 2?
Optic fibre endoscopes are used to examine the interior of a patient's body. These utilise the principle of total internal reflection and bundles of optical fibres.
Explain the phenomenon of total internal reflection and how the fibres are made to ensure this occurs. The fibre bundles can be coherent and incoherent. Distinguish between these and explain their uses in the endoscope.
Alpha, beta and ____ rays are among the products of ____ decay.
The order of penetration ability from the least penetrating to the most penetrating is: ~~y t~a ~~~
Radioisotopes are used in scanning because chemically they are to their non-radioactive equivalents and so enter into chemical processes.
Medical radioisotopes are usually administered by but in some cases by . The presence of radioactive particles is detected by ____ _ cameras.
The time for half the given mass of an element to decay into a new element is called its . This can vary from of seconds to ____ _ of years.
A commonly used medical radioisotope is ____ _
_____ -99m is the most commonly used radioisotope because it has a ____ _ half-life and is a pure emitter.
A PET scan uses _____ emitting radioisotopes.
When a positron meets an electron, a process called pair _____ occurs and the positron and electron are converted into two _________ _
A is a natural chemical substance labelled with a radioactive element for use in PET scans.
In a PET scan a atom from a radiopharmaceutical releases a ____ _ which interacts with an electron from the organ being investigated. The subsequent _____ rays are detected by special . The location ofthe initial positron and the number of rays can be detected, and from this an image of the organ is formed.
PET has the advantage over ultrasound and other imaging forms in that it can show organ as well as structure.
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Radioactivity is the spontaneous breakdown of an element into a new element by the emission of alpha (a), beta (p) and/or gamma (y) rays.
The table illustrates the properties of these radiations.
Type of Nature and Approximate Ionising Deflection in
Absorbed by electric or radiation charge mass effect magnetic field
helium nucleus, 4 x proton
alpha double positive strong sheet of paper very small charge
mass
beta electron, negative 1/1800 proton
weak 5 mm aluminium large positron, positive mass
electromagnetic very never fully absorbed,
gamma zero mass intensity halved by zero wave, neutral weak
25 mm lead
Radioisotopes - radioactive isotopes - can be used for body scanning. Chemically they are identical with their stable (non-radioactive) element and so take part in the normal metabolic processes of the body.
In isotope scanning, a radioisotope is introduced into the patient by intravenous injection or by inhalation. Special cameras - gamma cameras - allow the path and concentration of the radioisotope to be monitored. Abnormalities can thus be identified.
Radioisotopes vary in their half-life (the time for half the given mass to decay into a new element). These can vary from fractions of seconds to millions of years. It is important that medical radioisotopes have half-lives as short as possible so they do not cause (unnecessary) damage to the patient.
Commonly used medical radioisotopes include 1-131 (thyroid), Sr-85 (bone), Tc-99m (bone, thyroid, spleen, liver, etc.) and Th-201 (heart).
Tc-99m (technetium-99m) is the most commonly used medical radioisotope because it has a short half-life (6 hours) and is a pure gamma emitter.
Positron emission tomography (PET) is a non-invasive technique that uses positronemitting radioisotopes attached to biological chemicals (radiopharmaceuticals) to image the internal organs and tissues.
Pair annihilation occurs when a positron meets an electron. The proton and electron disappear and their mass-energy is converted into two gamma rays according to
+~e + _~e -7 2y. These gamma rays travel with the same speed in opposite directions. They can be used to determine the characteristics of the organ or tissue.
A radiopharmaceutical is a modified biological substance that is labelled with a radioisotope. 2-fluoro-2-deoxy-D-glucose (FDG) is similar to natural glucose but is labelled with the radioisotope fluorine-18. The rate of usage of FDG indicates the metabolic activity of an organ or part of an organ.
In a PET scan the patient is given a radiopharmaceutical. This is incorporated in the relevant organ and releases positrons that interact with electrons from the organ being investigated. The gamma rays are detected by special crystals situated in a doughnut shaped gantry into which the patient is placed. Since the gamma rays travel in opposite directions it is possible to determine both the location (where they were produced) as well as their number. Further computer analysis produces a visual representation of the organ.
PET is useful for determining the function as well as the structure of the organ being investigated. It is able to show the rate of uptake of a radiopharmaceutical and from this the functioning of the organ can be determined. PET is primarily used to investigate the brain including detection of tumours and strokes, for measuring blood flow and other neurological conditions such as Alzheimer's and Parkinson's diseases.
CHECKLIST - Can you: 1. Describe the properties of radioisotopes including their half-life? 2. Give example of medical radioisotopes? 3. Describe how medical radioisotopes are used? 4. Describe how positron emission tomography is done using positrons and pair annihilation?
It is found that 2~~U is the beginning of a long sequence of radioactive decays, each of which changes the nucleus involved to that of another element. Some of the steps in this decay series are shown following. Fill in the spaces denoted by'?'.
238 U -7 234rh + ? 92 90 .
2~6Th -7 ~Pa + _~e
iPa -7 23~U + _~e
23~U -7 ~Th + iHe
The table shows the half-lives for various radioisotopes. Which would be least useful for examination of a patient? Explain your reasoning.
Radioisotope Half-life
(-11 20.3 min
(0-60 5.3 years
Tc-99m 6 hours
Ga-67 72 hours
Positron emission tomography (PET) is a successful medical imaging technique. What is a positron? Where do these positrons come from? Clearly explain how a PET scan is done. What advantages does PET have over other imaging techniques?
The National Medical Cyclotron is situated in Camperdown, Sydney near the Royal Price Alfred Hospital. The two facilities are connected with a $500,000 pneumatic rapid transfer system. Explain why they are placed in close proximity.
A charged particle such as an electron or proton acts like a tiny ____ loop.
A fundamental property of elementary particles, such as mass and charge is its
A nucleus has a ____ determined by its ___ _
A proton has a net spin of ___ _
A top spinning about one axis will also revolve around a second axis. This is the phenomenon of ___ _
When placed in an external magnetic field, nuclei with spin: tend to align themselves parallel to the magnetic field tend to align themselves at right angles to the magnetic field.
The Larmor frequency is: the frequency of the applied magnetic field the frequency of the precession of the nuclei independent of the strength of the field.
Magnetic resonance imaging (MRI) uses ____ frequency energy and strong magnetic fields.
In an MRI scan frequency waves are directed at the body and are adjusted until occurs. At this frequency the RF energy is absorbed. When the RF is turned off the energy is and is detected by special receiving coils.
The properties of the tissue determine the signal and . Since different tissues have different densities, an image can be produced by a computer.
MRI is the number one imaging technique for studying the human ____ and central system.
Different scanning techniques all have their ____ and ___ _
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Protons, electrons, certain atoms and molecules act as tiny current loops; that is they act as tiny magnets. This effect is related to the spin of the charge as shown in the diagram. N N
Straight current-carrying wire Current loop Spinning charge
Magnetic fields associated with electric currents
Spin, like mass and charge, is a fundamental property of all elementary particles. It comes in multiples of 1/2 and can be + or -. Spin is a measure of the intrinsic angular momentum of an elementary particle.
Groups of particles also have a spin as a result of the spin of their individual particles. A nucleus, for example, has a spin determined by the spin of the nucleons that make it up.
For even mass number nuclei, the spin is an integer; for odd mass number nuclei
the spin is a half integer (~, ~ I ••• ). All nuclei with an even number of protons and
neutrons have zero spin in their ground state. A proton has a net spin of 1/2.
When set spinning about one axis - the axis of symmetry - a top will also rotate around a second axis. This change in the direction of the original axis of rotation is called precession.
Nuclei with spin tend to align themselves in an external magnetic field and precess about the field direction.
The precession rate - the Larmor frequency - is proportional to the applied field. Spinning top. As it spins around its
axis it also traces out a cone about a vertical axis.
Magnetic resonance imaging (MRI) is a non-invasive technique used to produce images of tissues inside the body using radio-frequency energy and strong magnetic fields.
In a MRI scan the patient is placed inside a powerful cylindrical magnet. The intense magnetic field forces nuclei in some of the atoms in the tissue being scanned (notably hydrogen) to 'line up'. Some of the atoms do not line up exactly with the field; rather they precess around it. Pulses of radio-frequency electromagnetic waves are then directed at the body and, if their frequency equals that of the nuclei - the Larmor frequency - resonance occurs. At resonance the nuclei absorb the radio wave's energy. When the radio wave is 'turned off' the nuclei return to their original orientation in the field releasing the absorbed energy as weak radio signals of the same frequency as the incident wave. A receiving coil detects this energy. Before the atoms have re-aligned, the field is changed from a constant field to a variable field - a gradient. Different atoms re-align to different strength fields giving out radio frequencies of slightly different frequency. Each frequency corresponds to a particular field strength and the latter can be localised to a particular location in the patient's body.
The strength and duration of the signals is dependent on the properties of the tissue from which they are emerging. The higher the spin density, the greater the concentration of hydrogen nuclei in the site being imaged. Hydrogen has its greatest density in body fluids. Next comes soft tissue followed by cartilage and membranes. Bones show no MRI signal. A computer decodes the signals into a visual image in a similar manner as for (T and PET scans.
MRI images are able to accurately differentiate between normal and diseased tissues and provide the most detailed anatomical information. MRI is the number one choice for studying the brain and central nervous system.
Different scanning techniques have different advantages and disadvantages.
CHECKLIST - Can you: 1. Explain the meaning of spin and how this leads to protons, electrons and some nuclei acting as tiny
magnets? 2. Describe the effect of applying a strong magnetic field to nuclei with spin? 3. Discuss precession and the relationship between the composition of the nuclei, the strength of the
magnetic field and the Larmor frequency? 4. Discuss the effect of directing radio waves at precessing nuclei? 5. Explain how an image is formed as a result of the relaxation of the nuclei?
Magnetic resonance imaging (MRI) relies on the spin of nuclei for its operation. What is meant by the 'spin of nuclei'? What is the significance of the fact that the hydrogen nucleus (proton) has the largest 'magnetic moment'?
Below is an MRI scan of a human head containing a healthy brain. Explain clearly how such a scan is made.
Magnetic resonance imaging is especially useful for imaging the brain and central nervous system. Why is this so much better than (T scans?
Explain four advantages of MRI?
The electromagnetic spectrum ranges from the high frequency rays to the low frequency waves. The Earth's atmosphere selectively __ _ certain frequencies from the spectrum.
Ground-based astronomy is restricted to which region/s of the electromagnetic spectrum?
visible visible, radio and some infrared visible and radio.
The light-gathering power of a telescope is a measure of its ______ . This depends on the of the lens or mirror.
The ability of a telescope to distinguish between two close objects is a measure of its ____ . This depends on the of the electromagnetic radiation used and the of the lens or mirror. It is measured in seconds of ___ _
The atmospheric effect that distorts the image of a distant light source is called ____ . This is a result of variations in the Earth's atmosphere's index.
Two techniques used to improve a telescope's sensitivity and resolution are ___ _ optics and ______ _
_____ optics samples the light from a distant source in real time and data is fed back to a _____ mirror that can be adjusted to minimise the image distortion.
Interferometry is a technique that uses the phenomenon of _____________ of electromagnetic radiation to study stellar objects. The device which consists of __ _ or more telescopes is called an _____ _
The sensitivity of a telescope depends on the of the lens or mirror; the resolution depends on the of the lens or mirror. Using interferometry can the resolution.
Lightweight mirrors, thin mirrors, replica mirrors and active optics are all examples of ___ generation telescopes.
Active optics compensates for: distortions in the atmosphere background light.
imperfections in the mirror
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The electromagnetic spectrum ranges from the high frequency (small wavelength) gamma rays through to the low frequency radio waves. These waves are selectively absorbed by the Earth's atmosphere. For example, ultraviolet and X-radiation are absorbed by the upper atmosphere and much of the infrared is reflected by water vapour and gases.
10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 10 102 103 104 (m)
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The electromagnetic spectrum
Ground-based astronomy is restricted to the visible and radio-wave regions of the electromagnetic spectrum with some narrow windows in the near infrared. For the other wavelengths we need to get above the atmosphere - we do this using telescopes like the Hubble Space Telescope (HST) and space probes.
The sensitivity of a telescope is a measure of its light-gathering power. This depends on the telescope's lens or mirror area (which depends on its diameter). The greater the area, the better the sensitivity.
The resolution of a telescope is a measure of its ability to distinguish between two very close objects. This is determined by the wavelength of the electromagnetic radiation used (the smaller the better) and the diameter of the lens or mirror. Bigger is better for telescopes! The resolution of a telescope is measured in seconds of arc (arc seconds) where there are 3600 seconds of arc in one degree.
The theoretical resolution of a telescope is rarely reached because of the phenomenon of seeing. This is the distortion of the image of a distant light source by the Earth's atmosphere. Seeing results from variations in the Earth's refractive index which cause a spot of light to 'wiggle' about randomly, distorting the image.
The sensitivity and resolution of a telescope can be improved by using the techniques of adaptive optics and interferometry.
Adaptive optics is a technique that involves measuring and compensating in real time for the atmospheric effects. By sampling the incident light up to 1000 times per second and measuring the amount of atmospheric distortion with a wavefront sensor it is possible to feed this information back to a wavefront correction device such as a 'flexible mirror' to effectively 'straighten out' the light. For it to work, adaptive optics requires a bright reference star to detect the distortion. Alternatively laser light is reflected off sodium atoms in the upper atmosphere.
Interferometry is a technique that uses interference of electromagnetic radiation to study objects. The arrangement of telescopes is called an interferometer. Light from a star enters two telescopes and is made to interfere. The type of interference fringes seen - constructive or destructive - depends on the different distances travelled to the two telescopes. This information can be used to construct an image.
The resolution of a telescope depends on the diameter of the lens or mirror but not the area (the sensitivity depends on the area). By constructing an interferometer with two separate telescopes the resolution can be enhanced. Interferometry is widely used with radio telescopes.
New generation telescopes use a variety of techniques including lightweight mirrors, spin casting, liquid mirrors, thin mirrors, replica mirrors and active optics. These all have the benefits of reduced cost relative to the quality of the mirror. lightweight mirrors can be made by 'digging out' some of the mirror's back or by casting mirrors with a honeycomb back. By spinning the molten glass as it solidifies - spin castinga depression forms in the middle which can be ground to the required shape. Thin mirrors can be made by producing -1 mm thick glass on a honeycomb composite backing structure.
Active optics compensates for imperfections in the actual mirror. The mirror is made up of many individual pieces, each of which can be controlled by actuators in a manner similar to adaptive optics. The difference is that the sampling is much less frequent for active optics.
CHECKLIST - Can you: 1. Describe the types and properties of the electromagnetic spectrum? 2. Define the meaning of the sensitivity and resolution of telescopes? 3. Explain the problems associated with ground-based astronomy as a result of the selective absorption
of certain wavelengths by the Earth's atmosphere? 4. Describe how adaptive optics and interferometry can be used to improve resolution and sensitivity of
telescopes? 5. Describe the techniques used in some new generation telescopes?
The two 10m diameter Keck telescopes are the largest reflecting telescopes in the world. They are situated at an altitude of 4,200 m on a mountaintop at Mauna Kea in Hawaii.
What quality/qualities is/are enhanced by having such a large diameter collecting dish? Explain your answer. What advantage(s) is achieved by placing the telescope at such a high altitude? Explain your answer. The 10 m mirror is made of 36 separate 1.8 m long hexagonal mirrors -7 cm thick and pre-stressed into the desired shape. What is the reason for this type of construction?
In 2000 the second Keck telescope was put into operation to be used in conjunction with the first (which was originally commissioned in 1992) as an interferometer.
What is an interferometer? What important property of telescopes is improved when it is connected as an interferometer? Explain your answer.
New generation telescopes have been designed over recent years to improve the effectiveness of telescopes. Clearly describe TWO such innovations explaining carefully what advantage they have.
Astrometry is the careful measurement of the position of celestial objects. This can be used to determine its from us.
The apparent movement of an object against a background when viewed from different positions is termed . This happens to stars when viewed from Earth at the extremes of its orbit around the Sun.
The distance to the nearest stars can be determined by __________ . This is limited by the size of its baseline which is the diameter of the Earth's around the Sun.
Astronomical distances are usually measured by astronomers in: parsecs light years both a and b arc seconds
The nearest star to us (other than the Sun) is Alpha Centauri. It has a parallax of 0.753 arc seconds. How far away from us is Alpha Centauri?
The speed of light is 3.0 x 108 m.s-1. How many metres are there in one light-year?
Trigonometric parallax is useful for determining the distance to: all the stars the few hundred nearest stars the few thousand nearest stars.
There are __ light-years in one parsec.
The astrometric satellite Hipparcos measured the of some 100,000 stars with an accuracy more than 100 times better than previous measurements. It was able to do this by getting above the Earth's _____ _
The data from Hipparcos led to a new estimate of the ___ of the universe.
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Astrometry is the measurement of the positions, motions and magnitudes of the stars. This allows the distance to the object to be determined when combined with other information.
Parallax is the apparent change in position of an object against a background when viewed from different positions. When the Earth rotates around the Sun the place where we view stars from continually changes. We can use this to determine the distance to these stars.
Earth
EOarth
Trigonometric parallax is the method used to determine the distance to the nearest stars. By measuring the angle of para \lax (p) in the diagram we can determine the distance by simple trigonometry. Its range is limited by the size of the baseline which is set by the diameter of the Earth's orbit around the Sun.
to Star
~---+------~P--7 ~ Ne~ Sun
star
Background stars
If p = 1 arc second, the distance to the nearby star is 1 parsec
The distances to the stars are measured in parsecs and light-years.
One parsec is the distance at which the radius of the Earth's orbit subtends an angle of one second of arc. If the parallax of a star (p) is measured in seconds of arc, then the
distance (d) in parsecs is given by d = ~ p
One light-year is the distance travelled by light in one year. It is equal to -9.5 x 1015 m. There are 3.26 light-years in one parsec.
The errors inherent in measuring the very small values of parallax means that trigonometric parallax is only useful for the approximately 100 nearest stars only.
The astrometric satellite Hipparcos has improved the measurement of the parallax of about one million stars by eliminating problems created by the Earth's atmosphere.
As a result of Hipparcos' measurements which showed certain stars, and therefore the galaxies in which they reside, to be -10% further away than previously thought, the age of the universe has been recalculated as -12 billion years.
CHECKLIST - Can you: 1. Define the terms parallax, parsec and light-year?
2. Solve problems using the equation d = ~ P
3. Describe how trigonometric parallax works and its limitations. 4. Describe the results obtained by the astrometric satellite Hipparcos.
Below is a diagram of the principle behind trigonometric parallax.
Earth
Sun
~ Ne~
star
Background stars
If P = 1 arc second, the distance to the nearby star is 1 parsec
Explain the meaning of parallax. Clearly explain how this method can be used to determine the distance to nearby stars? What limits the accuracy of this method? Explain your answer.
The star 40-Eridani has a parallax of 0.2 seconds of arc. How far away is 40-Eridani?
The astrometric satellite Hipparcos improved the accuracy of trigonometric parallax of some 100,000 stars by -100 times.
How was Hipparcos able to improve the accuracy? What did Hipparcos discover in its more accurate readings? What implications does this have for our view of the universe? Explain.
All of what we know about stellar objects comes to us as the object's _____ in the form of radiation.
Spectra can be _____ or _____ . They are viewed by devices called
Emission spectra can be continuous, _____ or ____ _
In a continuous spectrum, wavelengths are present. They are produced by solids, liquids and low-density gases when excited. True or false ____ _
Line emission spectra consist of: bright lines on a continuous spectrum dark lines on a continuous spectrum
bright lines on a dark background dark lines on a bright background.
Line emission spectra are produced when: an electron is excited to a higher energy level an electron falls from a higher energy level.
Absorption spectra are produced when: a continuous spectrum is passed through a hot gas a continuous spectrum is passed through a cool gas.
A spectroscope can spread light using a _____ or a _________ _
Stellar objects can be classified according to their spectra as ____ _ _____ ,' galaxies or q ____ _
Spectral _____ range from 0 to _____ with _____ being the hottest and the coolest.
Stellar spectra allow a range of characteristics to be determined including the star's structure, composition, velocity, and density.
Stars approximate to _____ and so their temperatures can be determined from the dominant _____ in the spectra.
The radius of a star can be determined by application of the Stefan-_____ Iaw.
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The spectra of stellar objects allow us to determine a lot of information about the object such as its surface temperature and chemical composition. This spectrum is in the form of electromagnetic radiation (visiblel infraredl ultravioletl radiol etc).
Spectra can be either emission or absorption spectra and are detected and measured by devices called spectroscopes.
Emission spectra can be either continuous, line or band.
In a continuous spectruml all wavelengths are present. Solidsl liquids and very dense gases produce these spectra.
When an element is excited by
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gas whose spectra is being investigated
Emission spectra composed of bright lines on a dark background
Formation of line emission spectrum
Molecules tend to emit band spectra rather than individual lines.
Line emission spectra are produced when an electronl excited to a higher energy level by heat or electricitYI falls back to a lower energy level emitting a photon of light given by the Planck relationship !1E = hf. This photon corresponds to a particular frequency or wavelength (colour).
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Just as an element is capable of emitting certain frequencies of light, so too it is capable of absorbing these same frequencies, giving an absorption spectrum. When a continuous spectrum of light is shone onto a cool gas, certain frequencies correspond to energy differences in the gas that will raise an electron to a higher energy level, and so those frequencies are removed from the continuous spectrum leaving dark lines against a continuous
Collimating slit
Glass
Absorption spectra composed of dark lines on a bright background
Formation of absorption spectrum
background. The absorption lines correspond to the emission lines of the elements, so allowing the elements present to be identified.
A spectroscope is a device for visually observing spectra. A spectrograph photographs or records the spectra. (The photographic image is called a spectrogram.) Spectroscopes can be either prism or diffraction types, both of which spread the light out into its spectrum.
source
Prism
pri~le
Prism spectroscope
Spectroscopes
Reflection grating
Slit
Diffraction spectroscope
Light source
Stellar objects can be classified according to their spectra as stars, emission nebulae, galaxies or quasars. Stellar spectra are absorption spectra, emission nebulae spectra are mainly hydrogen emission spectra (with some other elements), galaxies emit spectra across the range of the electromagnetic spectrum and are red-shifted, and quasar spectra are strongly red-shifted.
Stars can be further classified by their spectra into different spectral classes according to characteristics such as surface temperature. These classes are referred to as 0, S, A, F, G, K, M. Within each class there are 10 subdivisions (AO, A 1, ... , A9). These classifications are determined by the strength of the hydrogen absorption lines. 0 stars are blue and hottest; M stars are red and cooler.
Stellar spectra allow astronomers to determine characteristics such as the star's structure, chemical composition, velocity, temperature and density.
A star approximates to a black body and so there is a link between a star's colour and its temperature as shown in the graph. The hotter the star, the shorter the dominant wavelength emitted.
Stefan-Boltzmann's law can be used to deduce a star's composition and radius. This law states that the total amount of energy emitted by a hot body per unit surface area per unit time is proportional to the fourth power of its absolute temperature, that is £ = (J'P. But assuming the star to be a sphere, the luminosity is given by L = 4nW(J'T4 where R is the radius of the
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CHECKLIST - Can you: 1. Explain the production of emission and absorption spectra and compare them with a black body
spectrum? 2. Explain the operation of a spectroscope? 3. Describe the different types of spectra from stars, emission nebulae, galaxies and quasars? 4. Explain how stellar spectra can be used to classify stars? 5. Describe the information that can be deduced from spectra? 6. Explain the use of the Stefan-Boltzmann law to determine stellar radii? 7. Determine the temperature of a star from its black body radiation curves?
All we know about celestial objects comes to us in the form of the object's spectrum. What is meant by the term 'spectrum'? What are the two basic spectral types? State three pieces of information that astronomers can deduce from a stellar object's spectrum.
The diagram is a representation of the formation of a particular type of spectrum.
Collimating Glass slit
What type of spectrum is it?
Spectra composed of dark lines on a bright background
Clearly explain how this spectrum forms. Explain clearly how this of type of spectrum helps us discover information about stellar objects?
The spectral class of some stars is shown in the table.
Star Spectral class
Aldebaran K5
Betelgeuse M2
Deneb A2
Hadar B1
Which star is the hottest? Justify your answer. What is the likely colour of Betelgeuse? Justify your answer.
Clearly explain how the Stefan-Boltzmann law can be used to calculate the radius of a star. Equations may be useful in your explanation.
The measurement of the brightness of stars is: spectroscopy astrometry photometry.
The luminosity of a star depends on the _____ and the surface _____ of the star.
In addition to the factors in 2 above, the brightness of a star also depends on its _____ from us.
A star alpha has a magnitude of -1 and another star beta has a magnitude of +1. How much brighter is alpha than beta?
A star's brightness is determined by its _____ and _____ magnitudes.
The absolute magnitude is the brightness a star would have if it were placed __ _ pa rsecs from us.
Two identical stars alpha and beta exist with alpha twice as far away as beta. What is the ratio of the apparent magnitudes of alpha to beta?
The star Arcturus has an apparent magnitude of 0.00 and an absolute magnitude of -0.3. How far away is Arcturus?
Spectroscopic parallax: uses parallax to determine distances to stars does not use parallax to determine distances to stars.
The of a star is a measure of its magnitude measured separately through blue and yellow filters. This value is for blue stars and ___ _ for stars.
_____ tubes are used to measure low light intensities more effectively than _____ plates in photometry.
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Photometry is the measurement of the brightness of stars and other celestial objects. These measurements allow information about a star's temperature, composition, age, etc. to be determined.
Luminosity (L) is a measure of the rate at which a star emits radiant energy, that is, it is a measure of the total power emitted by a star. This depends upon the size of the star and its surface temperature.
The brightness (I) of a star is a measure of the intensity of radiation arriving at the Earth from that star. This is determined by three factors, the star's size (radius), surface temperature, and distance from us.
Brightness is given in terms of magnitude where a first-magnitude star is defined to be 100 times brighter than a sixth-magnitude star. It follows from this definition that the brighter the star, the smaller the magnitude and a difference of one magnitude
always corresponds to the same brightness ratio, that is, ~hoo = 2.512.
The brightness of a star determines its absolute and apparent magnitude.
The absolute magnitude (M) is defined as the brightness the star would have if it were a standard distance from us - this distance is 10 parsecs. This allows astronomers to compare stars in terms of characteristics such as their size and temperature. For two stars with absolute magnitudes MA and MB and apparent brightness IA and 18 respectively,
(MB-MA) we have IA = 100 -s-
IB
The apparent magnitude (m) of a celestial body is its magnitude as measured by an observer (usually on the Earth). For two stars with apparent magnitudes m
A and m8
respectively and intensities IA and 18 we have:
m B -mA =2.5log1O~' This is equivalent to IA =2.S(mB -mA)
IB IB
The magnitude of a star can be used to deduce the distance to the star. For a star with an apparent magnitude m at a distance d and absolute magnitude M at a distance
d of 10 parsecs it is found that m - M = 510g10 -
10 m - M is called the distance modulus.
Spectroscopic parallax uses stellar spectra to determine distances (it does not actually use parallax). Astronomers determine its spectral class and luminosity from its observed spectrum and place it on the Hertzsprung-Russell diagram to determine its absolute magnitude. By comparing this with its apparent magnitude, the distance can be calculated.
The colour index of a star is the difference between the magnitude measured using a blue filter and the magnitude using a yellow filter that is, CI = B - V. Blue stars have a negative colour index, red stars a positive colour index.
Photometry relies on photomultiplier tubes and photographic plates. Photomultiplier tubes convert weak light into easily measurable electric currents. They provide faster measurements of magnitude than photographic plates which rely on visual comparisons of the star images.
CHECKLIST - Can you: 1. Define absolute and apparent magnitude and how these can be used to determine the distance to
celestial objects?
2. Solve problems using the formulae m - M = 510910 ~ and ~ = 2.5(ma-mA)? 10 '8
3. Describe the principles behind spectroscopic parallax? 4. Define colour index and explain how it is used? 5. Compare the use of photomultiplier tubes and photographic plates in photometry?
The apparent magnitudes of some celestial objects are shown in the table.
Object Apparent magnitude
Moon -12.6
Sirius (brightest star) -1.4
Vega 0
Venus (max) -4.4
What is meant by the term 'apparent magnitude'? Which celestial object in the table appears brightest to us? Explain your answer. Compare the brightness of Venus with that of Sirius. Show your working.
The absolute and apparent magnitudes of various stars are shown in the table.
Star Apparent magnitude Absolute magnitude
Spica +1.00 -2.4
Castor +1.59 +1.0
Pollux +1.16 +1.0
What is the significance of the fact that Castor and Pollux have the same absolute magnitudes but different apparent magnitudes? Explain your reasoning. Which star has the greatest luminosity? Explain your answer. How far away is Castor?
The spectral class of some stars is shown in the table. Which star has the most positive colour index? Explain your reasoning.
Spectroscopic parallax is a method used to determine the distance to certain stars. Clearly explain how this is done.
Star
Aldebaran
Betelgeuse
Deneb
Hadar
Spectral class
K5
M2
A2
B1
Binary or multiple stars make up a significant proportion of all stars known. True or false? ___ _
Binary (or multiple) stars can be eithervisual, ____ , spectroscopic or ____ _ binaries.
In a visual binary, _____ stars are visible through a telescope orbiting in ellipses around a common of mass.
In an binary, the motion of one star leads to variations in the ____ _ of the light from the star.
Spectroscopic binary stars are recognised by their periodic doubling of the ____ _ lines as the stars periodically and from the Earth.
In binaries only one of the pair is visible. The presence of the other is deduced from its on the orbit of the visible component.
Two stars in a binary pair orbit their common centre of mass with a period of 3 years. They have an average separation of 3 astronomical units. What is their mass in units of solar mass?
Stars whose brightness changes either regularly or irregularly are called ___ _ stars.
Cepheids are _____ yellow stars whose brightness varies with a regular pattern.
The first Cepheid to be investigated and to have its ____ curve plotted was 0-___ _
For Cepheids, as the period of the light variations increases: the brightness increases the brightness decreases the brightness is unaffected.
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Binary stars consist of two stars orbiting about their common centre of mass and obeying the law of universal gravitation. About half of all known stars are binary or multiple stars.
Binary stars can be visual, eclipsing, spectroscopic or astrometric binaries.
Visual binary stars have orbits around a common centre of mass which can be directly observed as ellipses traced out against the background stars. Both stars are visible.
In eclipsing binary stars one of the pair eclipses (moves in front of) the other at regular intervals leading to variations in the brightness of the light from the eclipsed star as in the diagram.
Duller star
Eclipsing binary stars
A
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i U Brighter star I I eclipses \ I I duller star ,
i eclipse) DUII::tar ~ I (secondary \,
- eclipses brighter
I star (primary eCIiPse~
Time
Light curve for total eclipse (flat bottom)
Duller star eclipses brighter star (primary eclipse)
Time
Light curve for partial eclipse (V shape)
In spectroscopic binaries the Doppler shift in their spectral lines is used to determine their presence. This is characterised by a periodic doubling of lines as the stars recede and approach the observer at regular intervals as in the diagram.
I t
Red
Red shift <1(--
Violet
~--D~ []JI[
Spectroscopic binary stars and their spectra
---.,.. Blue shift
In astrometric binaries only one of the pair is visible. The presence of the other is deduced from perturbations in the orbit of the visible star.
Binary stars can be used to determine stellar masses using the formula
4n2r 3 m,+m2 = 2
GT
Variable stars are stars whose brightness varies either periodically or non-periodocally. They can be intrinsic variables or extrinsic variables such as eclipsing binaries.
Cepheids are supergiant yellow stars (of which approximately 1000 are known) which vary in brightness with an amplitude of about one magnitude and with absolutely regular periods.
8-Cephei was the first Cepheid to be investigated and its light curve is shown in the diagram. The brightness varies as the star undergoes alternating contraction and expansion.
A definite relationship exists between the period and the luminosity of a Cepheid. The longer the period, the greater the luminosity. This period-luminosity relationship of Cepheid variables can be used to deduce the distance to distant galaxies. By observing the period, the absolute magnitude can be deduced. Comparison with the apparent magnitude allows the distance to be calculated.
CHECKLIST - Can you:
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@ Type II Cepheids ~ - W Virginus stars
o RR Lyrae stars
5 10 50 100 Period (days) on a log scale
Period-luminosity relationship
1. Classify binary stars according to their means of detection as visual, eclipsing, spectroscopic or astrometric?
2. Describe how binary stars can be used to determine solar masses?
4n2r 3
3. Solve problems using m 1 +m 2 = GT 2 ?
4. Describe the different types of variable stars as intrinsic or extrinsic and periodic or non-periodic? 5. Explain how the period-luminosity law for Cepheids can be used to determine stellar distances?
Binary stars come in a number of different forms. Clearly distinguish between visual binary stars and spectroscopic binaries.
The diagram is of a particular type of binary star combination.
What type of binary star is it? Explain your reasoning. Clearly describe what is happening at the regions marked X, Y and Z in the diagram.
(J) (J) Ql c: :E Ol
&i
Time
Two stars in a spectroscopic binary have a period of 1.5 years and a separation of 5 AU (1 astronomical unit = 1.5 x 1011 m). Calculate the combined mass of the star system in kilograms.
Back in 1912 Henrietta Leavitt, an American astronomer measured the period of Cepheid variable stars in the Small Magellanic Cloud. Her results when plotted gave a graph similar to that in the diagram.
What is a Cepheid variable?
Given that 8-Cephei has a period of -5.4 days and an average absolute magnitude of -3.5, determine the distance to the Small Magellanic Cloud. Explain your reasoning.
12
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20
-0.5 o 0.5 1.0 1.5 log P
P is period in days
Period-luminosity curve
By examining star clusters astronomers can determine the _____ of stars.
Clusters can be either _____ or ____ _
_____ clusters are young clusters containing stars with relatively high percentages of metals.
_____ clusters are old clusters. They contain evolved stars like _____ giants and white ____ _
A Hertzsprung-Russell diagram is a plot of absolute magnitude or ____ on the vertical axis against temperature or class or index on the horizontal axis. It can be used to examine the of stars.
Compared to lower mass stars, larger mass stars: evolve slower evolve faster evolve at the same rate.
The birth of a star begins in a rarefied gas and dust cloud with a chance ____ _ that causes gas to attract more particles. Heat is generated by the conversion of ____ potential energy. The star first appears on the top right-hand of the Hertzsprung-Russell diagram but slowly works its way to the ___ _ sequence. Where it joins this is determined by the star's
A main sequence star burns _____ to form in its core in either the __________ chain or the cycle. The more massive the star, the _____ it consumes its fuel.
A star of -1 solar mass evolves into a ____ _ _ ____ when it comes to the end of its hydrogen burning phase.
For a star of -1 solar mass, the next stage (after red-giant) in its life cycle is as a: white dwarf neutron star black hole
For stars of -8 solar masses, elements up to can be synthesised in the core.
Iron core collapse leads to a core with a diameter of -20 km to form a star.
A hole may result if the core mass exceeds -3 solar masses in which case the contraction proceeds until the density becomes so high that even cannot escape.
On a Hertzsprung-Russell diagram, the lower the cut-off point the older/younger the cluster. ____ _
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Stars are born, mature and eventually die. By examining closely linked groups of stars known as clusters, astronomers can determine the evolution of stars.
Clusters can be either open (galactic) or globular.
Open (galactic) dusters consist of loose irregular aggregations of stars. There are a few hundred to a few thousand stars in each cluster. They are young clusters.
Globular dusters are tightly packed collections of hundreds of thousands or even millions of stars. They are old clusters containing evolved stars such as white dwarfs and red giants. Unlike open clusters, globular clusters contain little or no gas and dust that are the precursors of new stars.
The evolution of stars can be tracked on a Hertzsprung-Russell (H-R) diagram. This is a graph that plots two stellar properties on its axes. These properties include luminosity (and absolute magnitude) versus temperature (and stellar class or colour index).
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+10
White dwarfs +15 I I
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Main seq (Jet)
0(9
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1000
100
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50000 25000 11000 7500 6000 5000 3500 (Temperature K)
Hertzsprung-Russell diagram
The way in which stars evolve is determined by their mass. The greater the mass, the faster they evolve.
The birth of a star is literally clouded in mystery. Stars form from local condensations of cold, extremely rarefied gases and dust globules called proto-galaxies. A chance disturbance can cause gas to aggregate; this attracts even more gas. Conversion of gravitational potential energy into heat raises the temperature of the gas cloud.
The temperature can rise sufficiently to cause the cloud to emit a faint red glow. The protostar now appears on the H-R diagram in the top right-hand corner. Further contraction results in high enough temperatures for nuclear fusion to commence. The star eventually joins the main sequence - exactly where is determined by the mass.
A main sequence star is one in which hydrogen is 'burnt' to form helium in its core. There are two possible reactions - the proton-proton chain (in cooler stars) and the carbon cycle (in hotter stars). Stars spend the vast majority of their lifetime on the main sequence. The more massive the star, however, the faster it consumes its supply of hydrogen.
When a star of -1 solar mass reaches the end of its hydrogen burning phase it evolves into a red giant. These are large diameter, very luminous stars with a relatively cool surface emitting light in the red section of the visible spectrum.
For stars with mass -1 solar mass, helium burning is the last step in the nuclear reactions. The star ejects up to one-fifth of the original mass as a planetary nebula. The remaining mass collapses into a white dwarf. These are low mass, high-density very faint stars with no nuclear reactions proceeding.
For stars of initial mass greater than 8 solar masses, nuclear fusion reactions continue beyond helium burning. The helium core burns to form carbon and oxygen. These too can fuse to form neon, magnesium, silicon and sulfur; the silicon and sulfur can unite to form nickel and iron.
When the iron-core mass approaches 1.4 solar masses (the Chandrasekhar limit) the iron core collapses to a diameter of -20 km and the star blows itself apart as a supernova. It is during this time that elements above iron are synthesised.
The remaining core may form a neutron star of incredible density, or for stars whose core exceeds 3 solar masses, the collapse continues, forming a black hole only a few kilometres across. At these densities light itself cannot escape.
The H-R diagrams for open and globular clusters differ in their appearance. For a globular cluster there is a definite 'turn off' point where the star leaves the main sequence to become a red giant. These plots allow the age of a cluster to be deduced - the lower the turn off point the older the cluster.
CHECKLIST - Can you: 1. Describe the evolution of stars from their birth to their death? 2. Distinguish between the types of nuclear reactions in main sequence and post main sequence stars? 3. Describe the synthesis of elements in stars? 4. Describe how the age of a cluster can be determined from its Hertzsprung-Russell diagram? 5. Explain the meaning of planetary nebulae, supernovae, white dwarfs, neutron stars/pulsars and black
holes in relation to stellar evolution?
The diagram is a representation of a Temperature (degrees K)
Hertzsprung-Russell diagram for an 30000 10000 6000 3000 open cluster. -10
What is an 'open cluster'? What nuclear processes are going on -5 in the region marked Y? Clearly describe three characteristics 0
x
of the types of stellar objects found y
in region X. +5
The known elements are all made in stars +10 z in the process of nucleosynthesis. Describe how the elements up to and including iron +15 are made in stars and how the elements 0 B A F G K M beyond iron are created.
Clearly describe the evolution of a massive star (greater than 8 solar masses) from its birth to its death.
The Hertzsprung-Russell diagram for a range of clusters is shown in the diagram.
What is the significance of the lines leaving the main line and going diagonally up to the right?
Which cluster is the oldest? Explain your answer.
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In Rutherford's scattering experiment, alpha particles were fired at a sheet of gold foil. These alpha particles:
all passed through with little or no deflection were all deflected through large angles mostly passed through with little deflection but some had large deflections.
The Rutherford model of the atom pictures the atom as comprising a dense positive core or surrounded by orbiting with most of the atom being ____ space.
The Rutherford model was unable to explain what prevented the orbiting electrons from falling into the and producing a spectrum as classical physics predicted.
Line emission spectra: are unique to each element consist of dark lines on a continuous coloured background both a and b.
The alpha line in the hydrogen spectrum is produced when an electron falls from n = 3 to n = 2. What is the wavelength of this line?
Planck hypothesised that energy is that is, it comes in lumps or photons. What is the energy of the photon emitted in 5 above?
Bohr postulated that: electrons can exist in stationary states photons are emitted when the atom absorbs energy and the electron moves to a higher orbit both a and b.
Bohr's postulates enabled him to explain the ____ of atoms and the ___ _ spectrum of hydrogen.
Bohr's model was unable to explain some aspects of spectra including the spectra of larger atoms, the relative of the spectral lines, the existence of ___ _ spectral lines and the effect.
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In 1911 Geiger and Marsden conducted what became known as the Rutherford scattering experiment. Alpha particles were fired at a sheet of thin gold foil. Most of the alpha particles passed through with only small deflections as expected on the model of the atom current at that time but about 1 in 8000 were deflected through angles greater than 900
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As a result of the scattering experiment, the Rutherford model of the atom was proposed that pictured the atom with a dense positive nucleus (accounting for the large deflection of some particles) surrounded by electrons. Most of the atom is empty space (accounting for the lack of deflection of most particles).
The Rutherford model, however, left many questions unanswered such as what is the nucleus made of? what stops the electrons being attracted into the positive nucleus giving rise to a continuous spectrum and at the same time causing the atom to collapse? how electrons are arranged around the nucleus?
As far back as 1752 it had been shown that when an element is excited ,it emits light of definite wavelengths giving rise to a line emission spectrum when viewed through a spectroscope (see diagram), rather than a continuous spectrum of colours as seen when light is passed through a triangular prism. Different gases give rise to different spectra - the spectrum is unique to the element. Of particular interest was the line emission spectrum of hydrogen.
The Rutherford model of the atom
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1885 Johann Balmer found an empirical formula which gave the wavelengths of the emission lines for hydrogen. Written in its modern form Balmer's formula can be
written as ~ =RH (~-~) where RH is the Rydberg constant (1.097 x 107 m-1).
A, 2 n Additional series were subsequently found which fitted the more general equation
1 (1 1) A, =RH --2 --2 where nf = 1, 2, 3, 4, ... and nj = nf + 1, nf + 2, nf + 3, ... The line nf ni
emission spectrum of hydrogen was central to the Bohr's model.
In an attempt to explain the radiation curves of black bodies which could not be explained by classical physics, Planck postulated that energy came in 'lumps' or quanta given by E = hf. After successfully explaining black body radiation, the next triumph of the quantum theory was in explaining atomic spectra.
In 1913, to account for discrepancies in the Rutherford model of the atom and to explain line emission spectra, Neils Bohr made a number of postulates. He postulated that: electrons could revolve in certain energy states (levels) without radiating energy; when an electron falls from a higher energy level to a lower energy state it emits energy given by the Planck relationship t:.E = hf (see diagram); angular momentum (mvr) is
quantised and can only take values of nh 2rc
Bohr was successful in explaining the stability
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n = infinity n=6 n=5 n=4 n=3
n=2
n=1
of atoms and the existence of line emission spectra by these postulates. Using them he was able to derive the formula for the emission lines of hydrogen.
For all its successes Bohr's model was unable to explain a number of things including: it was an ad hoc mixture of classical and quantum physics; it only worked for atoms with one electron such as hydrogen; it could not explain the relative intensities of the emission lines; it could not explain the presence of hyperfine spectral lines and it could not explain the Zeeman effect - the splitting of spectral lines in a magnetic field. A new model was required.
CHECKLIST - Can you: 1. Describe the Rutherford model of the atom? 2. Explain the significance of the hydrogen spectrum to Bohr's atomic model? 3. Discuss Planck's contribution to the Bohr model of the atom? 4. State Bohr's postulates and discuss how these led to a mathematical model of the spectral lines of
hydrogen? h . 1 (1 1) 5. Use t e equation -=R H -2 --2
/L n f nj 6. Discuss the limitations of the Bohr model for hydrogen?
The diagram represents the apparatus used by Geiger and Marsden in the famous Rutherford scattering experiment. Clearly describe the results of the experiment and Rutherford's interpretation of these results.
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Gold foil
The violet line in the Balmer spectrum of hydrogen results from the transition of an electron from the 6th energy level to the 2nd energy level.
What is the wavelength of the violet line? What is the energy of the photon corresponding to this colour?
Bohr made a number of postulates about the structure of the atom. State TWO of these postulates and clearly explain what characteristic they were attempting to explain.
Bohr's model was successful in explaining some observations of the spectra of hydrogen but was unable to explain other spectral characteristics. State THREE phenomena that it was unable to explain.
Light exhibits wave characteristics like ____ and particle characteristics like the ____ effect. Light has a wave-particle ___ _
In 1924 de Broglie postulated that matter exhibits this same ___ _
What is the wavelength of an electron of mass 9.1 x 10-31 kg travelling at 2.0 x 106 m.s-1?
Davisson and Germer successfully demonstrated electron ____ by bombarding matter with electrons. This provided evidence for their nature.
In 1928 G.P. Thomson obtained a diffraction pattern by: passing electrons through thin metal foil passing alpha particles through thin metal foil.
de Broglie's matter waves helped explain: the line emission spectra of hydrogen the stability of atoms.
Werner Heisenberg put forward the principle as well as introducing a mathematical model for mechanics.
Pauli's exclusion principle helps explain: the regularity in the periodic table the line emission spectra of hydrogen.
Pauli predicted the existence of the: neutron neutrino quark nuclear fission.
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Light exhibits both wave properties, for example interference and particle properties, for example the photoelectric effect. Light is said to exhibit a wave-particle duality.
In 1924 the Frenchman Louis de Broglie postulated that all matter has this same wave-particle duality. That is, matter exhibits some characteristics of particles such as mass and momentum and some of properties of waves such as interference and diffraction.
de Broglie's matter waves have a wavelength given by
A, = ~ =!!.- where h is Planck's constant, m is mass and v is velocity. p mv
For electrons moving at -106 m.s-1 this wavelength is _10-15 m, comparable to interatomic spacing in crystals. This means it is possible to demonstrate the wave nature of matter by observing wave phenomena such as interference and diffraction.
In a series of experiments commencing in 1923 the Americans Davisson and Germer successfully demonstrated electron diffraction by bombarding a metal crystal with electrons (see diagram) - the electrons were exhibiting wave characteristics.
In 1928 G.P. Thomson (whose father J.J. Thomson had earlier proven the particle nature of electrons) passed a beam of electrons through a thin metal foil and obtained a diffraction pattern (see diagram) similar to that obtained by passing light through certain materials. This provided additional evidence for the wave nature of electrons.
In his model of the atom, Bohr had been unable to explain why electrons could revolve around the nucleus without radiating continuous energy and collapsing (his first postulate). He knew they did because matter existed. Matter waves could explain the stability these electron stationary states. If an integral number of electron waves fitted into the circumference of the orbit as in the diagram, a
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V
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stationary wave would be set up and no energy would be lost. (This can be shown also to lead directly to Bohr's third postulate but now there was a physical basis for it. For example if the radius of the orbit is rand n is an
integer then nA= 21[r and since A = ~ = ~ by combining
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t ese equations we get -- =21[r mv
p mv
nh =:> mvr =-
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Werner Heisenberg made important contributions to quantum theory, in particular his uncertainty principle. This states that for an elementary particle like an electron, the more precisely the position is determined, the less
Three wavelengths fit into the third energy level
Electron stationary waves
precisely the momentum at that moment is known (and vice versa). This effectively means that quantum mechanics is non-deterministic. (Classical physics said that if you know the position and momentum of an object at some time, then it is possible to predict its position and momentum any time later deterministic physics). Heisenberg also introduced a mathematical model for quantum mechanics.
In 1924 Wolfgang Pauli put forward the exclusion principle. This says that no two electrons can occupy the same quantum state of an atom. This principle explains the regularity in the periodic table of elements.
Pauli also predicted the existence of the neutrino.
CHECKLIST - Can you: 1. Describe de Broglie's proposal of the wave-particle duality of matter? 2. Solve problems using JL = hlmv? 3. Describe how Davisson and Germer confirmed de Broglie's proposal? 4. Use de Broglie's hypothesis to explain the stability of electron orbits? 5. Describe the contributions of Heisenberg and Pauli to the development of the atomic theory?
In 1924 Louis de Broglie proposed the wave-particle duality of matter. What is meant by wave-particle duality? Upon what basis did de Broglie have to make this proposal?
A moving electron of mass 9.1 x 10-31 kg has an associated matter wavelength of 8.0 x 10-10 m. What is the speed of the electron?
Davisson and Germer provided evidence for de Broglie's suggestion of the wave nature of electrons. Describe the experiment and how it gave this evidence.
Bohr was unable to explain the stability of electrons in their orbits around the nucleus of an atom. Explain how de Broglie's hypothesis provided an explanation.
A good microscope needs good and good power. The latter is dependent on the wavelength. The shorter the wavelength, the better the ___ _ power.
Electron microscopes use the ____ nature of electrons. These electrons are focussed by lenses. Their wavelength means they can distinguish smaller objects.
Electron microscopes work like ____ microscopes except they use ___ _ waves instead of waves and lenses instead of glass lenses.
The two basic types are _____ electron microscopes and _____ electron microscopes.
Electron microscopes can be used to view: live specimens only dead specimens only either live or dead specimens.
A TEM is analogous to a ____ light microscope.
In a TEM the electrons are transmitted through a thin specimen where they are absorbed ____ . The transmitted beam is focussed by a lens and are detected on a screen or a plate. They are able to create a ___ _ dimensional image.
A SEM is analogous to a _____ light microscope.
SEMs work by having a beam of electrons focussed onto a spot on the specimen where they emit electrons which control another beam creating an image.
To work, SEMs need to be coated with a _____ . They can produce ___ _ dimensional images.
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With the unaided eye the smallest object we can focus on is -0.1 mm. A good optical microscope can magnify this by -1500 times. Magnification alone is not enough, we also need to distinguish between two close objects - that is to resolve them - and this is dependent on the wavelength used. The smaller the wavelength the better the resolution.
Electron microscopes utilise the wave nature of electrons to provide enormous magnifications and improved resolution. A beam of high-speed electrons is produced and magnetic lenses are used to focus the beam. Their high speed means that they have a small wavelength and hence good resolving power (-1000 times better than light microscopes).
Electron microscopes work in an analogous way to light microscopes except they use electrons instead of light and magnetic lenses instead of glass.
Electron microscopes come in two basic forms - transmission electron microscopes (TEM) and scanning electron microscopes (SEM).
Because air will deflect electrons, the interior of electron microscopes is a high vacuum. This means that no live specimens can be observed.
A TEM is analogous to a transmission light microscope (except it uses electron waves instead of light waves).
In a TEM, electrons are transmitted through a very thin specimen (less than 100 nm thick) and the different materials in the specimen absorb the electrons differently. The transmitted electrons are focussed by a magnetic lens and are detected by a phosphor screen or a photographic plate. They produce two-dimensional images.
A SEM is analogous to a reflecting light microscope.
In a SEM an electron beam is directed onto a spot on the specimen and secondary electrons are emitted. The secondary electrons control another beam inside a video screen creating an image.
SEMs require that the sample be coated with metal (a conductor) prior to viewing. They produce three-dimensional images.
CHECKLIST - Can you: 1. Explain the application of the wave nature of electrons in electron microscopes? 2. Describe the principle of operation of electron microscopes? 3. Explain the high resolving power of electron microscopes?
Briefly describe the principle of operation of a transmission light microscope.
What are the advantages of an electron microscope over a light microscope? Explain your answer.
When bombarding beryllium with alpha particles in 1930, the Germans Bothe and Becker found:
gamma rays were emitted an unknown penetrating radiation was emitted.
In 1932 James Chadwick applied the laws of conservation of and ___ _ to this radiation and proved it to be composed of particles with a mass similar to that of a and with charge. These particles were ___ _
What is the composition of the nucleus of the element 2~~U?
The spontaneous breakdown of an element into another element is called ___ _ This can be natural or . The conversion of one element into another is called ___ _
Complete the following nuclear equation 1jN + iHe -7 ;0 + 1H
To create new isotopes, Fermi and his co-workers bombarded elements with: alpha particles electrons protons neutrons
Fermi was first to notice the splitting of the nucleus. True or false? ____ _
The creation of multiple neutrons in nuclear fission leads to the possibility of producing a reaction.
Pauli proposed the existence of the neutrino to explain: a discrepancy between the mass-energy before and after alpha decay a discrepancy between the mass-energy before and after beta decay the mass defect.
Nucleons are held together with the short-range _____ force.
The mass of an atom is greater than the sum of the masses of its parts. True or false?
The stability of an atom is determined by its: binding energy binding energy per nucleon
An atom bomb is an example of an chain reaction.
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In 1930, the Germans Bothe and Becker discovered that bombarding beryllium with alpha particles produced a very penetrating type of radiation. At first it was thought that this may be gamma radiation but subsequent investigation showed this to be incorrect.
In 1932, the Englishman James Chadwick suggested that this radiation might be the neutral neutrons postulated previously by Rutherford to explain certain properties of the nucleus. Subsequently Chadwick discovered the neutron by using the apparatus shown in the diagram. The radiation from the beryllium underwent collisions with the proton-rich paraffin and the protons were subsequently detected. By application of the laws of conservation of
?
Radioactive Beryllium source in lead block
Paraffin block
Neutron discovery
Detector
energy and momentum Chadwick was able to prove the existence of the neutron.
A nucleus consists of positive protons and neutral neutrons. The protons and neutrons
are collectively called nucleons. Elements are symbolised as t X where A is the mass number (the sum of the protons and neutrons) and Z is the atomic number (the number of protons).
Radioactivity is the spontaneous breakdown of an element into a new element by the emission of alpha and/or beta and/or gamma radiation. This can be natural or artificial. Transmutation, the conversion of one element into another, occurs in natural
radioactivity and can also be induced. In alpha decay we have t X ---7 ~=iY + jHe
and in beta decay we have t X ---7 Z ~ Y + Je + v where v is a particle called an
anti neutrino or t X ---7 Z j Y + +~e + v where v is a neutrino.
The first artificial transmutation was achieved by Rutherford in 1919 when he bombarded nitrogen gas with alpha particles to produce oxygen according to the
equation 1jN + iHe -7 1~O + ~H
Between 1934 and 1938, the Italian Fermi and co-workers bombarded many of the known elements with neutrons and created new isotopes, many of which were radioactive. When bombarding uranium-238 Fermi believed they had created the first transuranic element with atomic number 93.
The Germans Hahn and Strassman repeated Fermi's experiments and discovered
evidence ofthe presence ofthe element 1:iBa after bombarding uranium-235.ln 1939 the Austrians Meitner and Frisch stated that the neutron had split the uranium-235 nucleus into two halves - the process of nuclear fission. The reaction they investigated
was 235U + In ~ 141 Ba + 92 Kr + 3 1n + energy 92 0 56 36 0
The presence of more than one neutron in the products of the fission reaction meant that a chain reaction might be possible. Fermi was the first to demonstrate a nuclear chain reaction from nuclear fission in 1942.
In 1930 Wolfgang Pauli proposed the existence of a particle with properties unlike anything known at the time. It would have no electric charge, no mass, and no magnetic properties and would have almost no interaction with matter. It would, however, have energy, linear momentum and angular momentum. Fermi labelled it the neutrino'little neutral one' in his native Italian. When investigating beta decay, Pauli found that when the masses before and after were measured, and the difference in mass was converted to energy according to Einstein's E=mc2
, a discrepancy arose. On average one-third of the energy that should be associated with the electron disappeared - and nothing could be found to make up the deficit. Pauli suggested that the energy that appeared to be 'lost' was carried away by the neutrino. Without Pauli's postulated particle, the well-established laws of conservation of energy, mass and angular momentum would have to be abandoned - an idea that did not sit well with Pauli.
Nucleons (protons and neutrons) are held together by the strong nuclear force. This is an extremely strong. short-range force that acts equally between proton-proton, proton-neutron and neutron-neutron.
It can be shown that the mass of the atom is less than the sum of the masses of its components (protons, neutrons and electrons)! This difference is called the mass defect.
Mass defect is converted into binding energy according to E = mc2
• Th is is the energy required to separate an atom into its individual components. The binding energy per nucleon (BElA) is a measure of the stability of a nucleus. The higher the BElA the more stable the nucleus. A graph of BElA is shown.
o 20 40 60 80 100 120 140 160 180 200 220 240 Mass number
Binding energy per nucleon versus mass number
Chain reactions can be or uncontrolled depending on how many neutrons are available for the next fission (see diagram). An atom bomb is an uncontrolled reaction; a nuclear reactor is controlled.
o o
o
=====~n ----iI>n
=====fn n
=====fn
Uncontrolled nuclear reaction Controlled nuclear reaction
CHECKLIST - Can you:
o Uranium atom • 0 fission products
Nuclear fission reactions
1. Describe Chadwick's discovery of the neutron using conservation laws? 2. Define transmutation and explain how it occurs in natural radioactivity? 3. Describe Fermi's observation of a nuclear chain reaction?
n neutron
4. Discuss Pauli's experimental evidence that led to the prediction of the existence of the neutrino? 5. Compare the gravitational and electrostatic forces in the nucleus and explain the need for the strong
nuclear force? 6. Define mass defect and binding energy and calculate their values in nuclear reactions? 7. Compare a controlled nuclear fission reaction with an uncontrolled reaction?
The diagram is a representation of Chadwicks' experiment that led to the discovery of the neutron. Clearly explain the significance of the paraffin block and how Chadwick proved the existence of the neutron.
?
Radioactive Beryllium Paraffin source in block lead block
Between 1934 and 1938 Enrico Fermi and his co-workers bombarded many of the elements with neutrons.
What was formed as a result of this bombardment? Complete the following equations for one of the reactions that Fermi . . d 65 1 7C h 7C 7Z 0 investigate 29CU + on ~ ? u t en ? u ~ 30 n + -1e
What type of decay does the resulting copper nucleus undergo?
In 1930 Pauli hypothesised the existence of the neutrino. a State THREE properties of neutrinos. b Explain why Pauli made this prediction.
Calculate the mass defect and binding energy for a nucleus of ljN given the following rest masses proton = 1.007276 u, neutron = 1.008665 u, nitrogen-7 = 14.00307 u.
Atomic bombs are examples of uncontrolled nuclear reactions; nuclear reactors are controlled (we hope!). Distinguish between these two types.
Nuclear fission reactors release energy at a _____ rate. The heat is used to boil water to produce to turn turbines to drive to produce electricity.
Thermal reactors are the most common type of reactor. True or false? ____ _
In addition to a core of fuel, reactors have a ____ _ _ ____ rods, coolant and shields.
Most reactors use _____ uranium where the proportion of U-· _____ is increased to improve the of a fission occurring.
_____ slow down the neutrons to thermal energies. Examples include heavy water, _____ and beryllium. The control rods control the of the chain reaction.
The coolant absorbs: neutrons heat gamma rays.
Radioisotopes are _____ isotopes that find use in industry and medicine as radioactive used to follow particular chemical, and physical pathways.
In medicine they can be used in isotopic and in radiotherapy (radiation therapy). Different organs different isotopes and this can be detected with _____ cameras. For example, 1- is used to detect thyroid problems.
_____ scattering is a useful technique to investigate the internal structure of bulk matter. The penetrate more easily than charged particles.
_____ activation analysis is a method used where stable elements are made radioactive by bombarding with and detecting the characteristic energies of the em itted rays.
The Project was the name given to the development of the ___ _ bomb in World War II.
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le)!6oI0!q 'sJa)eJ:j.aA!peO!peJ q a:j.eJ 'a:j.!4deJ6 'SJo:j.Rlapow (fi:j.!l!qeqoJd) a)ue4) 'S£<:: 'pa4)!Jua UO!:j.e!peJ 'IOJ:j.uO) 'Jo:j.eJapow anJ:j. slo:j.eJaua6 'wea:j.s 'paIlOJ:j.uO) :SJaMSUtf
Nuclear fission reactors (see diagram) release energy at a controlled rate and use the heat from the reactions to boil water to make steam to drive turbines to drive generators to produce electricity.
Reactors can be either thermal reactors or fast reactors. In thermal reactors the neutrons have energies comparable to gas molecules at normal room temperatures. Most reactors are of this type. In fast reactors the neutrons have higher energies.
Reactor core with control rods
Coolant
Pump Heat exchanger
Nuclear power station
Condenser
Thermal reactors have a core of fuel, moderator, control rods, coolant and radiation shields.
Most therma I reactors use enriched uranium as the fuel where the proportion of U-235 is increased to improve the probability of fission occurring. (U-235 is fissionable with slow (thermal) neutrons more readily than U-238.) A critical mass is required for fission to occur.
Moderators slow down neutrons to thermal energies which prove better at initiating fission reactions. They include ordinary water, heavy water, graphite and beryllium; materials that do not readily absorb neutrons. The control rods on the other hand work by absorbing neutrons and in this manner control the speed of the reaction. Materials used include cadmium and boron.
The coolant absorbs the heat from the reaction and is used to generate steam to drive the turbines that drive the generators. Radiation shields protect the walls of the reactor and the reactor personnel from exposure.
Radioisotopes (radioactive isotopes) find extensive uses in industry and medicine. By attaching radioisotopes to various materials it is possible to trace their movement and storage in chemical, biological or physical systems. Industrially these radioactive tracers can be used to do a range of jobs from measuring wear in machinery to controlling the thickness of metals or plastic during manufacture.
Medically the isotopes can be used in isotopic tracing/scanning and radiation therapy. In isotopic tracing/scanning a patient is given a specific radioisotope. Different
organs take up this isotope in different amounts and this can be detected by gamma cameras. For example, I-131 is used to detect abnormalities in the thyroid and technetium-99m to detect abnormalities in the bone and lungs. These have short halflives. In radiotherapy radioisotopes like Co-60 are used in cancer treatment with the emitted gamma rays being used to kill cancerous cells.
Neutron scattering is an effective way to probe inside bulk matter. Because it has no charge, the neutron can penetrate more easily than charged particles and interact with matter by being scattered - diffracted. Unlike X-rays that scatter well off high atomic mass atoms with lots of electrons, neutrons scatter off low mass atoms including hydrogen (proton) which makes them ideal in determining the structure of solids containing hydrogen bonds which includes all organic and many inorganic molecules.
In neutron activation analysis (NAA) certain stable elements are made radioactive by bombarding them with neutrons. These radioactive elements then decay and the emitted particles have energies that allow them to be readily detected. For example,
stable sodium atoms can be activated by neutron capture: HNa + 6n ~ ~1Na + y.
The 24Na nucleus then decays to give sodium, y-rays, electrons and neutrinos. The electrons have a characteristic spread of energies and the y-rays have specific energies. Sodium can thus be detected by the presence of lines at these energies in the gamma ray spectrum of the irradiated material. NAA is particularly useful in the analysis of the rare earth elements, uranium, barium, thorium and hafnium.
The Manhattan Project was the code name for the development of the atomic bomb during WWII. The discovery by German scientists of nuclear fission in 1938 prompted a number of physicists including Einstein to encourage the American President Franklin D. Roosevelt to push for the development of the atomic bomb before the Germans could develop one. Led by Robert J. Oppenheimer the project - the costliest ever to that time - successfully developed the U-235 bomb which was dropped on Hiroshima and the Pu-239 bomb dropped on Nagasaki leading to the surrender of the Japanese.
CHECKLIST - Can you: 1. Describe the operation of a nuclear fission reactor? 2. Describe some applications of radioisotopes in industry and medicine? 3. Explain the advantages of neutron scattering to investigate the structure of matter? 4. Assess the significance of the Manhattan Project?
Nuclear fission reactors are used to produce heat from a controlled nuclear reaction. Most reactors are thermal reactors that use enriched uranium as the fuel. They also have a moderator and control rods as well as a coolant and radiation shields.
What is a thermal reactor? What is enriched uranium and why is it used? Describe the function of the moderator and control rods and explain how they achieve their task.
Radioisotopes are extensively used in industry and in medical applications. Explain what radioisotopes are? Describe how these can be made artificially? Describe one industrial and one medical use of radioisotopes.
Neutron scattering is an effective way of investigating the structure of bulk matter. What property do neutrons have that enable them to penetrate matter more easily than protons? What advantage does neutron scattering have over X-ray diffraction for investigating matter? Explain your answer.
The Manhattan Project was the code name for the World War II production of the atomic bomb. Discuss the significance of its success and the consequences for society.
?
The stability of a nucleus is determined by the value of the ____ _ per nucleon. To disrupt a stable nucleus physicists use particle ____ _
Two examples of the devices mentioned in 1 above are: _____ and ____ _
The model of matter attempts to explain the interaction of subatomic particles with the exception ofthose involving . It has two main components: the theory and quantum ____ _
This model divides matter into three families __________ and ____ _
The three families can be further classified as _____ particles or force-____ _ particles.
Fundamental particles with charges that are fractions of the electronic charge are: gluons muons quarks.
Hadrons are particles composed of two or more . Two ____ _ combinations are called and three combinations are called
Protons and neutrons are examples of . These interact through the _____ nuclear force.
Mesons are made from a quark and: one other quark two other quarks an antiquark
Leptons are massive subatomic particles. True or false? ____ _
Bosons are: gauge particles matter particles a type of quark
High energy physics is strongly lined with _____ which seeks to explain the structure and existence of the ____ _
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The stability of a nucleus is determined by the value of the binding energy per nucleon. The larger this value the more stable the nucleus. To investigate the nuclear force and the nature of the fundamental particles, the nucleus needs to be disrupted. To do this energy must be put into the nucleus. Physicists use particle accelerators to probe inside atoms.
Particle accelerators include Van de Graaff generators, cyclotrons, betatrons, synchrotrons and linear accelerators.
The standard model of matter is a theory that attempts to describe all interactions of subatomic particles (excluding gravity). This model has two components: the electroweak theory which describes interactions through the electromagnetic and weak nuclear force; and quantum chromodynamics which is the theory of the strong nuclear force.
This model divides matter into three families - quarks, leptons and bosons.
E
MATTER
Leptons
e.g. electron, neutrino, muon
Hadrons (composite particles made up of quarks)
Baryons (3 quark composite e.g. proton, neutron)
I Mesons I I (quark and antiquark
composite e.g. pion)
Gauge particles e.g. photon, gluon
These three families can be further classified as matter particles (quarks and leptons) or force-carrier particles (bosons) as in the diagram. A classification scheme for matter
Quarks are fundamental particles with charges -ie and}e . There are six varieties
(flavours) of quarks grouped into three pairs: up/down, charm/strange or top/ bottom as in the table.
Quark (q) Symbol lepton (I) Symbol
up u electron e-
down d electron-neutrino V. strange s muon If
charm c muon-neutrino v p
bottom b tau r
top t tau-neutrino V;
Quarks do not exist in isolation but are always combined with other particles. Hadrons are composite particles made of quarks. Hadrons are divided into baryons (three quark combinations) and mesons (two quark combinations).
Baryons include protons and neutrons. Protons are made of two up quarks and one down quark. Neutrons are made of one up and two down quarks. Baryons interact through the strong nuclear force.
Mesons are combinations of a quark and an antiquark. Mesons are unstable and decay in millionths of seconds.
leptons are particles with little or no mass. They do not experience the strong force. Rather they interact through the weak force (and charged leptons also interact through the electromagnetic force).
The four fundamental forces - gravity, electromagnetic, strong nuclear and weak nuclear - are carried by force-carrier particles - bosons (also called gauge particles). They are gravity by the graviton (this is still to be discovered), electromagnetic by the photon, strong nuclear by the gluon (this keeps quarks together) and weak nuclear by the weakon (weak boson).
Cosmology seeks to explain the universe's structure and existence; it requires quantum mechanics to do this. During the first 10-35 seconds after the Big Bang, temperatures were so high that three of the fundamental forces of nature (the strong nuclear, weak nuclear and electromagnetic) were combined into one force. Study of high-energy physics may lead physicists to an understanding of the moment of creation!
CHECKLIST - Can you: 1. Explain the need for particle accelerators? 2. Describe the main features of the standard model of matter? 3. Explain the link between cosmology and high-energy particle physics?
Particle accelerators are devices vital to the study of high-energy physics. What are particle accelerators? Clearly explain why they are required by physicists?
Briefly describe the standard model of matter.
High-energy particle physics and cosmology are closely related. Explain why this is so.
The examination is divided into two sections, Section I and Section II.
SECTION I Total marks 75 This section has two parts, Part A and Part B.
Part A Total marks 15
All questions are compulsory. Each question is worth one mark. Questions are mUltiple-choice. Select ONE letter from the alternatives A, B, Cor D. Answer on the multiple choice answer sheet provided. Allow approximately 30 minutes for this part.
Part B
Total marks 60 All questions are compulsory. Questions have a range of marks. (The number of questions may vary each year but will continue to be worth 60 marks.) Questions are extended response. The mark value is indicated alongside each question. There may be a number of parts to a question while others require a more integrated answer. Answer in the Part B answer book. Allow approximately 1 hour 45 minutes for this section.
SECTION II Total marks (25)
Attempt ONE question only. The question is divided into parts with the mark value indicated alongside each part. Answer in the writing book provided. Allow approximately 45 minutes for this section.
The Physics Formulae Sheet and Physics Data Sheet provided with the HSC examination have been reproduced on pages 150-151. The Periodic Table of Elements appears on the inside front cover.
Total marks 15. Questions 1-15. All mUltiple choice.
Select the alternative A, B, Cor D that best answers the question.
The gravitational potential energy of a satellite in orbit above the Earth/s surface is: negative because it has escaped from the Earth/s gravity positive because it is above the Earth negative because it is defined to be zero at infinity positive because it is defined to be zero at infinity.
A plane flying horizontally with constant speed drops a food package to a group of bush walkers isolated by floodwaters. The plane continues to fly horizontally after the package is dropped. Relative to the plane and neglecting air resistance, the package lands:
directly below the plane directly below the point of release in front of the plane behind the plane.
Multistage rockets are used to place satellites in orbit because: it is easier to manufacture rockets in separate stages the reduction in mass as each stage is jettisoned increases the acceleration of the rocket the reduction in mass as each stage is jettisoned decreases the acceleration of the rocket the reduction in mass as each stage is jettisoned increases the thrust of the engines.
Communication with distant spacecraft is affected by: the distance to the spacecraft the Van Allen radiation belts sunspot activity all of the above.
The Michelson-Morley experiment attempted to: measure the speed of light measure the speed of the Earth through the ether show that the speed of light is constant and is independent of the motion of the source or the observer disprove the existence of the ether.
Two parallel current-carrying wires are separated by a distance d and exert a force per unit length of F newtons per metre. If the separation between the wires if reduced to d/2, the force per unit length is now:
4F 2F F/2 FI4
The south pole of a magnet is brought towards a circular metal ring that hangs freely from a vertical string as shown. Looking towards the ring:
current is induced in a clockwise direction and the ring is attracted to the magnet current is induced in a clockwise direction and the ring is repelled by the magnet current is induced in an anticlockwise direction and the ring is attracted to the magnet current is induced in a anticlockwise direction and the ring is repelled by the magnet.
In a step-down transformer:
Permanent magnet being moved towards the ring
Aluminium or copper ring
the voltage in the secondary is less than the voltage in the primary the voltage in the secondary is greater than the voltage in the primary the power in the secondary is greater than the power in the primary the current in the secondary is less than the current in the primary.
Electric power is transmitted at high voltages (as high as 500 kV) because: it is easier to generate electricity at higher voltages than at lower voltages the electricity gets to its destination faster at higher voltages the higher voltages mean lower currents and so lower energy losses in the transmission wires higher voltages create smaller eddy currents in the transformer cores resulting in lower energy losses.
The electric motor used in small appliances in the home is most likely to be: a single phase AC induction motor a three phase AC induction motor a DC commutator motor an AC synchronous motor.
This question refers to the diagram. The apparatus shown is used to demonstrate that cathode rays:
are electrons carry energy and momentum cause glass to emit X-rays travel in straight lines.
Maltese pross
/
Electrodes
J
The threshold frequency for copper is 1.1 x 1015 Hz. When ultraviolet light of frequency 3.2 x 1015 Hz is shone on the same copper plate, the maximum kinetic energy of the emitted electrons is:
1.39 x 10-18 J 7.26 X 10-19 J 2.11 X 10-18 J zero, since no electrons would be emitted.
Doping of semiconductors with a group III element: results in conduction by electrons only results in conduction by holes only causes the conductivity to increase causes the conductivity to decrease.
Silicon rather than germanium is the preferred semiconductor in electronics because: it is easier to make smaller devices with silicon than germanium silicon is more abundant than germanium germanium is harder and so it is more difficult to work with than silicon germanium has a lower 'leakage current' than silicon.
The Maglev experimental train relies for its operation on: the photoelectric effect the Doppler effect the Zeeman effect the Meissner effect.
Total Marks 60. Questions 16-27.
Show all relevant working in questions involving calculations.
The following data may be required to answer some of the following questions. Mass of Earth = 5.983 x 1024 kg Radius of Earth = 6.38 x 103 km G = 6.67 X 10-11 N.m2.kg-2
A fully equipped astronaut weighed 1200 N on Earth. What would an identical astronaut weigh on Mars where the acceleration due to gravity is 3.8 m.s·2?
It is a remarkable indication of scientific achievement every time a manned spacecraft successfully blasts off into orbit. It is an even more remarkable feat to bring the astronauts safely back to Earth. Clearly describe the major issues affecting a safe re-entry of the spacecraft and what is done to ensure the success of the re-entry.
A stone is projected horizontally out to sea from the edge of a cliff 100 m high. Given that the stone is thrown with an initial speed of 10m.s·1 and neglecting air resistance find:
the time the stone takes to hit the water. the distance from the cliff base at which the stone hits the water.
International communications depend on the use of satellites placed in a geostationary orbit. This orbit lies at a distance of 42,300 km from the centre of the Earth.
What is a geostationary orbit? What orbital speed must the satellite have if it to remain in orbit? Calculate the acceleration due to gravity at this distance from Earth?
A spaceship passes you at a speed of 0.95c. To a member of the spaceship's crew, its length is 100 m. What length would you determine it to be? If you observed the spacecraft for one hour, how much time would a crew member determine to have passed? What are the implications for manned space flight from your answer to part b above? Explain your reasoning.
A schematic diagram of a simple DC motor is shown.
Split ring commutator
Carbon brush
Armature
Clearly explain how this simple motor works. State TWO ways in which the motor could be improved.
A schematic diagram a simple AC generator is shown.
Carbon brushes held in place by springs
Field magnets
~'\ \
\ ~
Clearly explain how this generator works. Sketch the output voltage for this generator, clearly explaining any characteristics. How could this output be converted into DC output? Explain your answer.
Eddy currents find uses in induction cookers and eddy current braking. What are eddy currents? Describe how these currents are used in induction cookers and in eddy current braking.
Transformers are used to boost the voltage generated from the power station from 11 000 V AC to as high as 500000 V AC for distribution to towns and cities.
Explain how a transformer works. Transformers are found in many home appliances. What function do they serve?
AC induction motors are widely used in the home. Briefly describe how these motors operate. State TWO reasons for the widespread use of these motors.
In 1897 J.J. Thomson used apparatus similar to that in the diagram to determine the charge to mass ratio for cathode rays. By suitably adjusting the strength of the electric and magnetic fields, Thomson was able to determine the speed of the electrons that reached the screen.
Explain how this was done?
Stream of
~F~=th~O~d;~;~=~ay~s,-~~~~~ I / : Collimator
Electron gun
I +
Coil to produce magnetic field
Given that the parallel plates were separated by 0.01 m and had a voltage of 200 V across them and the magnetic field strength was 0.001 T determine the speed of the electrons. What force acts on the electrons due to the magnetic field?
A schematic diagram of a cathode ray tube (CRT) is shown.
What is the purpose of the electron gun? Name a scientific device that uses CRTs. In what fundamental way would the CRT in a television differ from the one in the diagram?
Accelerating
Filament _ +
Grid
Electron gun
Deflection system
Site of evacuation
Fluorescent screen
/ Fluorescent screen
Solar cells are essential in providing electricity in satellites as well as in remote areas. They depend on doped semiconductor material and the photoelectric effect for their operation. Explain how solar cells work.
In 1915 Sir William Bragg and his son Lawrence were jointly awarded the Nobel Prize for Physics.
What did they do to deserve this award? Describe how they conducted their experiments and what they found.
The Dutch physicist Heike Onnes discovered the phenomenon of superconductivity in 1911.
What is superconductivity? Describe what happens to the resistance of a superconductor as the temperature is lowered clearly noting any point of interest. Describe one current or potential use of superconductivity. What is preventing the greater use of superconductors?
Total marks 25. Attempt ONE question from Questions 31-33. Allow about 45 minutes for this section.
Show all relevant working in questions involving calculations.
Question 31 - Medical Physics Question 32 - Astrophysics Question 33 - Quanta to Quarks
Ultrasound is a medical technique used for imaging organs in a patient. State FOUR advantages in using ultrasound for imaging. Explain why a coupling medium is placed between the ultrasound transducer and the patient's skin during an ultrasound examination.
Doppler echocardiography is an important diagnostic procedure. It relies for its operation on the Doppler effect.
What is the Doppler effect? Explain. Explain how echocardiography works?
The acoustic impedance of fat and kidney are 1.38 x 106 kg.m-2.s-1
and 1.62 x 106 kg.m-2 .s-1 respectively. What is meant by acoustic impedance? What is the ratio of the reflected to incident intensity for a fat/kidney interface? What does this tell you about the ability of ultrasound to distinguish between fat and kidney? Explain your answer.
Positron emission tomography (PET) is a non-invasive medical imaging technique. It relies for its operation on electron-positron annihilation.
Explain the meaning of 'electron-positron annihilation'. Clearly describe where the two components - electron and positron - originate. What is the advantage of PET over other types of scans?
Three commonly encountered medical conditions are bone fractures, monitoring of foetal development and stroke. Describe an imaging technique useful for each of these conditions, explaining clearly why you have chosen that particular method.
Ground based astronomy has a number of serious disadvantages. Describe ONE of these disadvantages and explain how astronomers attempt to overcome the problem.
Astronomers are continually asking for funding for bigger and bigger telescopes. What advantages do bigger telescopes have over their smaller counterparts? Explain you answer.
The star Canopus has an apparent magnitude (m) of -0.9 and an absolute magnitude (M) of -7.4. Why do these two magnitudes differ? Explain your answer.
The spectra of stars can be used to classify them. Describe how such a classification scheme works.
The distance to some stars can be determined by the method of spectroscopic parallax. Explain how this is done.
The table below shows some stars and some of their characteristics.
Star Apparent visual magnitude Absolute visual magnitude Spectral class
Arcturus 0.00 -0.3
Betelgeuse +0.41 -5.6
Hadar +0.63 -5.2
Sirius -1.51 +1.4
Vega +0.04 +0.5
Use this table to answer the following questions. Which star is the hottest? Justify your answer. What is the colour of Arcturus? Explain your answer. Which star is the faintest when viewed from Earth? Justify your answer. How far away is Hadar?
K2
M2
B1
A1
AO
Sirius, the brightest star in the sky, is an example of an astrometric binary. What is an astrometric binary? State the names of ONE other type of binary star systems and explain how it is recognised.
A teacher was overheard to say that 'the evolution of a star depends on its mass'. Discuss this statement.
For simple gases such as hydrogen, the frequency of any spectral line is simply the sum or difference of the frequencies of other spectral lines of the same gas. Use Bohr's model to account for this observation.
A hydrogen atom is excited causing its electron to jump from the ground state to the n = 3 state.
What is meant by the 'ground state'? How much energy is required for this transition?
In 1924 Louis de Broglie made a postulate (proposal) that was to revolutionise our understanding of matter.
What was de Broglie's postulate? Describe an experiment that provided evidence for this proposal.
The German Werner Heisenberg and the Austrian Wolfgang Pauli made significant contributions to our understanding of the atom. Describe the contributions of each of these physicists.
Technetium-99m (Tc-99m) is a radioisotope widely used in medical diagnosis. It has a half-life of 6 h.
What is a radioisotope? What is the advantage of Tc-99m having a relatively short half-life? Explain your answer.
The purpose of a fission reactor is to produce heat energy from nuclear fission in a controlled manner. Important components in such reactors include the fuel, the moderator, the control rods and radiation shielding. Briefly describe the purpose of each of these components.
The standard model of matter classifies matter as 'matter particles' or 'force-carrier particles'. The 'matter particles' can be further divided into two families.
What are these two families? Give an example of a particle which belongs in each family in i above. Give an example of a 'force-carrier particle' and the interaction that it mediates.
Gm b The acceleration due to gravity on a planet of mass m and radius r is given by: 9 = -. For alpha
r2
GM g=-2-' for beta
r
G(2M) GM g=--=2--, for gamma
r2 r2
G(2M) 2GM 1 GM g=--=--=--
(2r)2 4r2 2 r2
GM GM 1 GM g=--=-=-- and for delta
(2r)2 4r2 4 r2
693.9 N The mass on Earth is found from m = W = 2000 = 204.1 kg. Since mass is constant then the weight 9 9.8
on Mercury is found from W = mg = 204.1 x 3.4 = 693.9 N
c To remove a mass from near the Earth would require work to be done on it (to overcome the gravitational force of attraction between the two masses). That is, energy would need to be supplied. Adding a positive energy to a negative energy allows the final energy to be zero. By definition, the gravitational potential energy at infinity is zero.
The gravitational potential energy is given by Ep = -G mME where r is the distance between centres. r
S b t 't t' h E - G mME - 667 10-11 1000x5.983x1024
- 597 1010 J u S I U mg we ave p - - -- - -. x x - -. x r (6380 + 300) x 103
There is a whole range of experiments that could be done to determine g. Whichever method you used, your answer should include the following points:
the actual equipment you used, for example pendulum, falling mass, data logger ... how you conducted the experiment including taking multiple readings where appropriate the analysis of the data to determine a value for g, for example, if you used a pendulum you would
have solved the equation T = 27r{g where Tis the period ofthe motion, I is the length of the pendulum
and 9 is the acceleration due to gravity the potential sources of error.
As suggested in the hint, these problems are best solved by splitting them up into their two component motions - horizontally with constant velocity and vertically with constant acceleration.
For the vertical motion we have: u y = 500 cos 30 = 433 m.s-\ Vy = 0 (at maximum height) so
substituting into the equation for accelerated motion we have: v y 2
= U Y 2
+ 2ag L3.Y
0= (500 cos 30)2 + 2( -9.8)L3.y
4332
L3.y = -- = 9566.3 m 19.6
Note that the acceleration due to gravity is negative. This is because it acts in the opposite direction to the initial motion. The initial motion is generally considered to be the positive direction.
h . h h' h' h . f df Vy-Uy 0-500cos30 T e time to reac t IS elg tiS oun rom: Vy = Uy + agt => t = = = 44.2 s ag -9.8
The distance travelled horizontally is found from the horizontal component of the motion which is constant velocity. The time of flight is twice the time to reach the maximum height so:
ill< =U x t = 500 sin 30 x88.4 = 22100 m
The escape velocity is the minimum velocity required for an object to leave the gravitational pull of a planet (or moon). Escape velocity depends on the universal gravitational constant (G) and the mass and the radius of the
planet (or moon). (The actual relationship is ve = )2GME but is not required by the syllabus.) RE
Asthe hint suggested, this problem is solved by substituting the data into the equation for Kepler's law: r: = GM2 • T 4n
1 1
(GM )3 (6 67x10-11 x7 1x10
23 2)3 Rearrangingtofindrweget:r= 4n2XT2 =' 4n2
' x(1.09x105) =2.43x107m
The rocket is propelled by the emission of gases formed from the combustion of the fuel and oxygen. The engines produce a reasonably constant thrust and consequently the rocket accelerates in accordance with Newton's second law, F = mao The combined mass of the rocket and fuel decreases as the fuel is burned and the gases are ejected. Since the acceleration of the rocket is inversely proportional to the mass (a = Flm), the acceleration increases. Jettisoning of various stages in a multistage rocket also leads to increased acceleration.
Roller coaster rides are subject to g-forces like those experienced by astronauts when they travel through vertical loops. Consider a rider at the bottom of a loop (that we will consider to be the arc of a circle). Because he travels in a circle, he requires a centripetal force. This is supplied by the force of the seat
2 2
N W = mv => N = W + mv . The g-force is given by the ratio NIW. Depending on the speed v and the R R
radius R it is possible for the g-forces to be similar to those felt by astronauts.
Extended space travel is not currently feasible due to the relatively slow speeds of rockets attainable by present technology. It would take several years to travel to even our nearest planetary neighbours. This would require significant amounts of food, water and oxygen. The large payloads would require larger rockets for launch with associated costs. Weightlessness has associated health implications as evidenced by the condition of astronauts and cosmonauts when they return to Earth after extended stays on the orbiting space stations. In addition the psychological problems inherent in extended isolation from other people and family have to be considered.
The maximum speed in the universe is the speed of light. Although fast (3 x 108 m.s-1) it still takes time for the signals to travel to and from Mars. The time to travel to Mars is given by:
s 8x1010
t = - = = 267 s = 4 min 27 s v 3 X 108
The Van Allen radiation belts are two belts of energetic charged particles surrounding the Earth. They trap charged particles emitted from the Sun. Intense solar activity can disrupt the belts and radiation emitted by the charges (synchrotron radiation) can disrupt the communications between Earth and orbiting satellites.
The solar wind is associated with sunspot activity. When sunspot activity is highest, the charged particles in the solar wind increase and this affects the Earth's magnetic field which in turn affects radio communication.
Consider the diagram opposite representing the apparatus used by Michelson and Morley. The half-silvered mirror splits the light into two coherent beams - one beam travels across the ether and the other beam travels with and against the ether. The times to do this can be shown to be different and when the beams are recombined an interference pattern forms. By rotating the whole apparatus through 90° the beams can be interchanged and so a change in the interference pattern should occur. No change was observed. This meant that the motion of the Earth through the ether could not be detected.
Consider the diagram of an 'Einstein light clock'. Assume that a pulse of light travels from the bottom mirror and is reflected by the top mirror and travels back to the first mirror. Let this be one unit of time (say a 'tick'). Relative to an observer travelling with the clock, the light beam moves straight up and down. Relative to an observer who sees the light clock moving past them, the light follows a zigzag path. This path is longer than the straight up and down path. Since both agree on the speed of light being constant, then the stationary observer must conclude that the time in the moving train is going slower since time = distance/speed.
so by substituting the
relevant data we get: t = 2.2 = 49.2 J.1s ~1- (0.99ge i
e 2
Half-silvered mirror
Elherwind
Michelson-Morley experiment
Einstein 'light clock'
To accelerate a mass requires that we provide it with energy. But according to special relativity, energy and mass are related by E = me2
• The increasing energy leads to an increase in mass. According to Newton, as mass increases the acceleration decreases. The faster the mass is moving, the less will be the acceleration until the point is reached when the mass effectively becomes infinite and so no acceleration is possible. Thus the speed of e cannot be reached.
According to special relativity, time in a moving frame of reference (for example a rocket ship) goes slower than time in a stationary frame relative to an observer in the stationary frame. To an observer in the moving frame (the rocket ship), time goes 'normally'. For example, if one year passes in the rocket ship relative to a crewmember in the ship, more time will pass for an observer on Earth (2.3 years at 0.ge). If the
rocket returns to Earth it will return to the Earth's future. It is unlikely that this will occur because governments would be unwilling to spend enormous sums of money on something they would not live to see. Also astronauts would be unlikely to travel knowing their friends and relations would be dead on their return.
a Application of the right hand palm rule has the palm pointing up the page. (The particle will actually follow the arc of a circle when it is in the field.)
d The force per unit length between two parallel current-carrying conductors is given by: ~ =k 1,12 . If I d
one of the currents is tripled and the separation is doubled, the new force F' is given by:
F =k 1,312 xl="i xk 1,12 xl="iF 2d 2 d 2
a Application of the right hand palm rule for current flowing from A to B shows that the side AB experiences a downwards force.
Torque is a maximum when the plane of the coil is parallel the plane of the magnetic field.
Maximum torque is given by: r=nB1A =1500xO.8xO.1x5x10-2 x3x10-2 =0.18N.m
Note that the area of the coil is simply the length x breadth (as it is a rectangular shape) and the lengths have to be converted to metres. When the coil is set at 45° to the field, the torque is given by: r =nB1A cosS = 1500 xO.8 xO.1 x5 x 10-2 x3 x10-2 cos 45 = 1.8 x10-' N.m xcos 45 =0.127 N.m
As seen in the diagram, the moving coil meter consists of a current-carrying coil of wirf,! in a radial magnetic field. The coil thus experiences a torque causing it to turn. A fine wire spring gets 'wound up' until it stops the coil rotating - the bigger the current the more the coil twists and the further the pointer moves. The radial field ensures that the torque is always constant (the plane of the coil is always parallel to the plane of the field) allowing a linear scale for the meter.
For a current to be induced, there must be relative motion between the magnet and the coil. This means that either the coil be moved and the magnet held stationary, or the magnet moved into a stationary coil (or both can be moved). The induced current can be increased by ill moving the magnet (or coil) faster, b using a stronger magnet, or c using a coil with more turns.
Lenz's law says that the direction of the induced emf is such that the current it induces sets up a magnetic field in a direction to oppose the cause of the emf. If the direction of the induced emf aided the generation of the emf we could produce an infinite amount of energy from a finite amount of work. This would violate the law of conservation of energy which basically states that energy can be transformed from one form into another but cannot be created or destroyed.
Electric motors have an armature (a coil) and a magnetic field. As the armature rotates there is a change of magnetic flux through it and so an emf is induced in the coil- it acts like a generator. The direction of this back emf opposes the supply emf. The faster the armature spins, the greater the induced emf. At start up, the back emf is small and so the current through the armature can be large enough to cause it to burn out. By placing a starting resistance in series with the motor, the current can be kept within safe limits. As the motor speeds up and the back emf increases, the starting resistance can be removed.
In part b the disk stops because eddy currents are induced in the disk since there is a change of flux through the disk as it rotates. The direction of these eddy currents is such as to oppose the cause (Lenz's law). By placing slits in the disk as in part c, the eddy currents are reduced in size and so there is less opposition - the disk spins longer.
c The split-ring commutator changes the direction of the current each half-cycle.
2 3 4 5 2
Time
AC output
3
Commutator reverses current
DC output
4 5
Time
One complete turn
As the disk is rotated, there is changing magnetic flux through the disk and so an emf is induced. Because there is a complete circuit, current will flow. As long as the disk is rotated, current will be induced. You could consider the disk to be made of a large number of straight conductors like the spokes of a wheel. The movement ofthese 'spokes' between the poles of the magnet results in an emfbeing induced between its ends.
There is a whole range of points that might be stated here. They could include the following: Social implications
increased working hours (no longer determined by the hours of daylight) movement of population to the cities from the country easier communication the coming of the information age increased leisure time with time saving devices more 'entertainment' (radio, movies, TV, DVD, CD ... )
Environmental issues include: global warming because of combustion of fossil fuels pumping carbon dioxide into the atmosphere acid rain drowning of vast tracts of land for hydroelectric power stations alleged increases in cancer for people living near high voltage power lines.
c A step-up transformer steps up voltage but steps-down current (power is constant).
A transformer is used to transfer electrical energy between circuits and for changing the voltage (and current). Changing voltages applied to the primary circuit set up changing magnetic flux in the soft iron core (the core concentrates the flux). By mutual induction, this changing flux induces a changing emf in the
secondary coil. By varying the number of coils in the primary and secondary, the voltage (and current) can be changed.
The transformer equation is: V p =:!..e... = lL. Hence rearranging to find the secondary voltage we have: Vs ns Ip
V = ~ x V = 250 x 240 = 60 V s np p 1000
Eddy currents are induced in bulk conducting material placed in changing magnetic flux. In a transformer, these eddy currents would lead to heat being generated in the core, representing a waste of energy. This is minimised by laminating the core, that is, making the core out of individual sheets of metal other than one single piece.
Energy losses come about as a result of eddy current generation in the transformer core (see 3 above) and heat generated in the power lines. The latter can be minimised by keeping the current as low as possible. This means transmitting the energy at very high voltages (-500 kV). High voltage means low current in a transformer.
a The stator has the changing magnetic field produced in it - this induces current in the rotor.
d
Single-phase AC induction motors are widely used because they are simple in design, highly efficient (for example they don't require a commutator or brushes - these parts tend to wear out) and they are relatively cheap.
AC induction motors work on the principle that a rotating magnetic field in the stator will induce current in the rotor which sets up a second magnetic field. The two fields interact and the rotating field 'drags' the rotor around.
In this tube there are coloured streamers flowing between the anode and cathode and glows surround the anode and cathode. In this low pressure tube, no glow is visible in the gas in the tube but the glass at the end of the tube, opposite the cathode, has a green glow.
Tube 1 (the Maltese cross) indicates that cathode rays travel from the cathode in straight lines as shown by the formation of the shadow of the cross on the end of the glass discharge tube. Tube 2 (the 'paddle wheel') indicates that the cathode rays carry energy and momentum as shown by the movement of the wheel away from the cathode when it is turned on. The fact that something is hitting the paddle wheel is also indicated by the glow on the tips.
The role of the Thomson experiment was to determine the nature of cathode rays. Thomson believed them to be particles and reasoned that it should be possible to determine the ratio of their charge to mass. The uniform electric field (E) between the two parallel plates would produce a force (F) on the rays
given by F = qE = q V where q is the charge, Vis the voltage between the parallel plates and d is their d
separation. The magnetic field would exert a force on the rays that would cause them to move in the
2
arc of a circle that is: qvB mv =>!L = v . By arranging the fields in such a way that the electric R m BR
and magnetic forces were made equal, the rays would pass through the tube with no deflection, that
is q£ =qvB => v = ~. All quantities could be determined and so the charge to mass ratio could be B
calculated.
Lightning rods work by effectively discharging the highly charged cloud above the rod. Clouds tend to be negative at their base and this induces a positive charge on the ground and buildings under the cloud. Corona discharge, the flow of charge from a sharp point, lessens the charge able to build up on the building, so preventing a possible sudden discharge in the form of lightning. In a photocopier, a thin 'corona' wire sprays charge onto an aluminium drum coated with the metal selenium. Selenium conducts electricity better in light than in the dark - it is photoconductive. An image is projected onto the charged selenium surface. Where light hits the charge leaks away; and where no light hits the charge remains. This creates a latent image. Positively charged toner is then attracted to the negative charges on the drum's surface, forming a positive image. This is then transferred to a sheet of paper and heat rollers fuse the toner to the paper.
Hertz was investigating the generation and properties of electromagnetic waves (previously hypothesised by Maxwell). Hertz's apparatus consisted of a high voltage induction coil and a detecting loop of metal. Sparks from the induction coil produced sparks in the gap in the detector. By shining ultraviolet light onto the gap, Hertz was able to demonstrate that the gap could be made wider and a spark would still jump across the gap. Without the UV light, the spark could not be produced if the gap was made too big.
Electromagnetic waves are generated whenever charges are made to undergo accelerations. By connecting an AC supply to an aerial- essentially a conductor - electrons could be made to oscillate up and down the aerial. This would create a changing electric field, which would induce a changing magnetic field, which would induce a changing electric field ... A self-propagating electromagnetic wave would be the result.
Blackbody radiation curves could not be explained by the physics of Maxwell and Newton - the so-called classical physics. A whole new theory was needed. This was the quantum theory of Planck.
This is the critical (or threshold or cut-off) frequency, that is, the minimum frequency that would cause electrons to be emitted from the metal. Because 1.6 x 1014 Hz is above the critical frequency, electrons would be emitted from the surface of metal x.
When two or more atoms come close to each other interactions between the two or more nuclei and the electrons lead to a split in the energy levels. With billions of atoms this leads to a continuum of energy levels - an energy band. No forbidden energy gap in metals means that the valency band and conduction band overlap. This leads to large numbers of charge carriers being available for conduction, accounting for the high electrical conductivity of metals.
Germanium was originally the semiconductor of choice because it could be purified more easily than silicon. Purity is important in semiconductors. The discovery of how to purify silicon more easily, along with its wider abundance and lower leakage current, means that silicon is the preferred semiconductor today.
Doping occurs when a Group III or Group V atom is substituted for a Group IV atom in silicon or germanium. When a Group III atom is substituted for a Group IV atom there is one less electron present than there was previously. This missing electron is equivalent to a positive charge or 'hole'.
Thermionic devices are electronic devices that use thermionic emission to produce electrons. This is where materials are heated to literally 'boil' electrons off them. These electrons can then be used in devices such as diodes, triodes and pentodes. Solid state devices are electronic devices that use doped semiconductors to manipulate charges (electrons and holes). Solid state devices have all but eliminated thermionic devices because they can be made smaller, are less demanding on power, react faster and require no 'start-up' time.
d Materials only become superconducting below a certain temperature. This transition temperature is different for different materials.
a Freidrich and Knipping first demonstrated the regular arrangement of atoms in crystals using X-ray diffraction. The father and son team of W. and L. Bragg did extensive work on crystals using X-ray diffraction.
d The so-called high temperature superconductors still require temperatures of -134 K. These are very difficult to produce, especially on a large scale.
MRI requires intense magnetic fields. These are best produced by using electromagnets, consisting of superconducting coils in which large currents can flow with little resistance and so little energy loss.
The BCS theory of superconductivity states that as an electron moves through a crystal lattice it causes the lattice to become distorted. This distortion leads to an increased positive charge density which causes a second electron to be attracted to the first electron forming a 'Cooper pair'. This pair of electrons can pass unimpeded through the lattice so there is no resistance.
A piezoelectric crystal is one that will vibrate when connected to a high frequency AC supply. Conversely if the crystal is made to vibrate it will produce an alternating potential between its two faces. A high frequency AC supply is connected between the two faces of the crystal and this causes the crystal to vibrate at the same frequency. This sets up longitudinal waves in the air - ultrasound.
The frequencies used are a compromise between the ability to 'see' small objects - this requires small wavelengths (high frequencies) and the absorption and scattering of the ultrasound by the tissues (which is also increased for high frequencies).
The acoustic impedance of a medium is a measure of how easy it is for sound to be transmitted through the medium.
Z =pv =>p=~= 1.61x106 =1025.5kg.m-3
v 1570
The greater the difference in acoustic impedance between two materials means that more energy is reflected at the interface and little energy is transmitted. Transmitted energy is critical in forming the echoes from various interfaces to allow a scan to be produced. The large difference between air and muscle results in almost all the ultrasound being reflected from the interface and so no image can form.
/ [z -zt [(1.70 1.38)X106t .L = 2 1 = . This means that 1.08% is reflected and the rest is transmitted.
/0 [Z2+Z1t [(1.70+1.38)X10 6t
X-rays are high frequency electromagnetic waves. X-rays are produced when high-speed electrons are rapidly decelerated by allowing a beam of electrons to hit a target (such as tungsten). Hard X-rays have higher frequencies and penetrate matter further than soft X-rays.
Radiographs like that shown in the question are formed by allowing X-rays to pass through the area of the patient to be investigated and allowing the transmitted X-rays to fall on a photographic plate. The different absorption of the X-rays by different tissues means that various shadows are formed on the plate. This is a negative image - where most of the X-rays are absorbed, the plate is clearest, where least is absorbed the shadows are darkest.
A CT or CAT scan is an acronym for a computerised (axial) tomography scan. This non-invasive technique uses X-rays and computers to produce an image of internal organs. The patient is placed on a table that can slide into a circular scanning machine or gantry. X-rays are fired radially through the patient from different angles. Detectors on the opposite side to where the X-ray is fired measure the degree of absorption of the X-rays. This information is relayed to computers that generate an image of a 'slice' of the patient. By moving the patient along the axis of the gantry, a three-dimensional image of an organ can be formed. Whereas a simple radiograph has 32 shades of grey to form shadows, a CT scan can have 256 shades allowing for greater discrimination between different tissues.
When light travels from a less dense medium into a more dense medium an angle is reached (critical angle) beyond which the light is totally internally reflected. This means no light can leave the less dense material. Optical fibres consist of extremely thin glass fibres in a sheath of a more dense material. The light can be bounced along the tube even when the fibre is bent. In a coherent bundle, each fibre is kept in the same relative position at both ends of the bundle. This ensures that an image can be transmitted without distortion. In an incoherent bundle, the fibres are arranged randomly. They can transmit light to illuminate the tissue/structure that is to be viewed. The coherent bundle transmits the image back to the doctor.
iHe, 239~Pa, 239~Pa, 2~iu, 2~iu, 2~~Th
Co-60 would be the least useful because it has a long half-life. This means that it would continue to bombard the patient with radiation for many years increasing the likelihood of causing cancers by destroying/modifying cells in the patient.
A positron is a positive electron: +~e
Positrons come from radioactive atoms attached to various biological chemicals - radiopharmaceuticals - that are given to the patient. The patient is first given a positron emitting radiopharmaceutical such as FDG (like glucose) by intravenous injection (or by inhalation for some radiopharmaceuticals). The patient is then placed on a table that is placed in the circular PET scanner. Positrons emitted by the radiopharmaceutical interact with electrons from the patient's organ being investigated and pair annihilation occurs. The two gamma
rays produced travel in opposite directions with the same energy and are detected by a ring of crystal detectors. Computers determine the location where the gamma rays were produced and also their intensity. Further computer analysis enables a 'slice' of the organ to be displayed on a video monitor. By taking a number of adjacent slices, a three-dimensional image can be produced. PET has the advantage that it shows the functioning of an organ as well as its structure. For example, the functioning of the brain can be seen by the uptake of FDG (a radiopharmaceutical chemically identical to glucose).
The cyclotron is used to produce short half-life radioisotopes for use in medical imaging (and in radiotherapy). The short half-lives mean that the radioisotopes need to get to their destination as soon as possible before their radioactivity falls to levels too low to be of use. This requires the cyclotron and hospital to be placed close together.
Spin is a fundamental property of elementary particles. It comes in multiples of 1/2 and can be positive or negative. It is a measure of a charge's angular momentum. Tissues contain lots of hydrogen nuclei (protons) and it is the magnetic moment of nuclei that is measured in MRI. The fact that the magnetic moment of a proton is large makes it useful for scanning.
The patient is placed on a table that is moved into the centre a powerful circular magnet. The field of this magnet is some 30,000 times more intense than the Earth's magnetic field. This causes the protons to attempt to align in the intense field. The protons actually precess about the field. Pulses of radio-frequency electromagnetic radiation are then directed at the organ being investigated and if their frequency equals the Larmor frequency, resonance occurs and energy is absorbed. The radio waves are then turned off and the atoms relax and re-emit the radio-frequency energy. Special receiving coils detect this. By suitably arranging the main field and three other weaker fields, it is possible to pin-point the location where the RF energy is emitted. Since the strength and duration of the emitted signals is dependent on proton density which is determined by the tissue type, an image of the tissues can be produced by computers. This is the most sensitive scanning technique.
Although CT scans are better than normal radiographs for differentiating between different tissue types, nevertheless MRI is better still. In addition, MRI effectively 'sees through' bone as if it is not there making imaging of the brain and central nervous system easier.
MRI has the following advantages: no ionising radiation used, provides the clearest pictures, can be used to image of whole range of tissues and organs, best for the brain and central nervous system, can show function as well as structure (with functional MRI).
The two qualities affected by diameter are sensitivity and resolution. Sensitivity is a measure of the light gathering power - the larger the area (which depends on the diameter) of the collecting dish the more sensitive the telescope. Resolution is the ability to distinguish two very close objects. Again, the larger the diameter (the area is not important) the better the resolution. At such a high altitude the telescopes are above much of the Earth's atmosphere (and its pollution) and so the problem of 'seeing' is reduced. This is the effect of variations in the refractive index of the Earth's atmosphere that makes a spot of light 'wiggle about' causing the image to be unclear. It also gets the telescope away from background light from cities. The individual plates to the mirror allow for modifying the shape ofthe mirror to overcome imperfections (active optics) and to allow the telescope to compensate for 'seeing' using the principle of adaptive optics. In this, the light from a star is sampled and the amount of atmospheric distortion is measured. Corrections can then be sent to the flexible mirror to compensate for this distortion.
An interferometer consists of at least two separate telescopes whose signals are made to interfere. From the interference - either constructive or destructive - an image can be created. The resolution of the telescope can be improved by this technique. The resolution is determined by the diameter of the collecting dish (not the area). This can be increased by separating the two (or more) telescopes. Their separation then becomes the effective diameter. For example, the two Kecktelescopes are placed 85 m apart and act as one telescope with an 85 m diameter!
Your answer could include any two of the following: Adaptive optics (see 1c above) Thin mirrors - glass only -1 mm thick is attached to a honeycomb composite backing structure. This decreases the weight and construction cost of the mirror compared to older mirrors. Replica mirrors - by using an existing mirror as a template it is possible to make a mirror with the correct shape without having to regrind it thus saving money. A graphite reinforced composite material is applied to the mirror and after curing a thin reflecting surface is added. Active optics - similar to adaptive optics but used to compensate for imperfections in the shape of the mirror, allowing it to be made larger (with improved sensitivity and resolution). Liquid mirrors- rotating liquid mercury forms a parabolic mirror as it rotates. Capable of high performance.
Parallax is the apparent change in position of an object against a background when viewed from different positions. A star's position against the background stars can be viewed from different positions in the Earth's orbit around the Sun. The angle subtended at the star from the two extreme points is twice the parallax. A right angle triangle is obtained of which we know one side (the radius of the Earth's orbit) and one angle. This allows us to determine the distance to the star. The longer the baseline, the larger the parallax. Too small a parallax angle and it cannot be accurately measured. The baseline is limited by the diameter of the Earth's orbit around the Sun.
1 1 1 Distance and parallax are related by: d = -. Substituting we have: d = - = - = 5 parsecs.
p p 0.2
By getting above the atmosphere, Hipparcos was able to eliminate problems associated with distortions due to the changing refractive index of the atmosphere - the problem of 'seeing'. Hipparcos discovered that galaxies were actually further away than originally believed. Because the age of the universe is related to the expansion of the universe, the more accurate measurements enabled a more accurate determination of the age. It was calculated to be -12 billion years old.
A spectrum is the range of wavelengths (frequencies) of electromagnetic radiation coming from a source such as a star. Emission and absorption. Any three of: temperature, structure, chemical composition, rotational velocity, luminosity, density ...
An absorption spectrum. As a continuous spectrum passes through a cooler gas, some of the frequencies correspond to the energy required to excite an electron in the gas to a higher energy state. This effectively removes that wavelength (colour) from the spectrum so we end up with a series of dark lines on a continuous background of colours (if it is in the visible portion of the spectrum). The absorption lines are identical to the emission lines of various elements. By comparing the dark
lines with known emission lines it is possible to infer the presence of particular elements in the outer layers of the star's 'atmosphere'. The width of the lines allows us to infer the density and the fact that an absorption spectrum exists at all tells us about the structure of the star with a core surrounded by a cooler outer layer.
Hadar is the hottest star as it is a B 1 star. The hottest stars are 0 followed by B then A ... Betelgeuse is probably red in colour as it is a cool star as indicated by its spectral class as an M star.
The Stefan-Boltzmann law states that the energy emitted by a hot body per unit area per unit time is
proportional to the fourth power of the temperature that is E = aT 4 . If a star is considered as a sphere of
radius R, the luminosity is given by L = 4nR 2aT 4 . Luminosity and temperature can be determined from the spectrum and so the radius can be calculated.
The apparent magnitude is the brightness of a star when viewed from Earth. The moon appears brightest to us because it has the most negative magnitude. (The lower the number, the brighter the object.)
I Venus = 2.5(m Sirius-m
Venus) = 2.5(-1.4--4.4) = 2.53 . Venus is 15.625 times brighter than Sirius. I Sirius
Castor and Pollux are different distances from us which is why their apparent magnitudes are different even though their absolute magnitudes are the same. Spica has the greatest luminosity as it has the smallest absolute magnitude.
d d 0.59 d m-M=510g-; 1.59 1.00=510g- => --=Iog- => d =13.1parsecs
10 10 5 10
Betelgeuse. Positive colour indices correspond to red stars. The reddest star is Betelgeuse as it is an M2 star.
Spectroscopic parallax has nothing to do with parallax! From its spectral class and luminosity the position of the star on a Hertzsprung-Russell diagram can be determined. From the diagram the absolute magnitude can be estimated. This, along with the apparent magnitude that can be measured by photometry allows the distance to be calculated.
a In a visual binary star both components are visible orbiting around their common centre of mass. In a spectroscopic binary the two components cannot be resolved as individual stars by telescopes but their presence is indicated by the Doppler shift of their spectral lines leading to a periodic doubling of the lines.
This is an eclipsing binary as indicated by the type of periodic variation in the light intensity. At X and Z the brighter star is being eclipsed by the duller star. That is, the duller star is moving in front of the brighter star. At Y the brighter star is eclipsing the duller star.
The equation relating mass to the motion of a binary is m 1 +m 2 = 4n2
r 3 where mass is in kg, radius is in GT
metres and period is in years.
Substituting into this equation we get m 1 +m 2
2 ( 11)3 4n 7.5 x 1 0 047 k -----'----:-:--~ =1.11 xl g 6.67 X10-11 x1.52
A Cepheid variable is a supergiant yellow intrinsically variable star whose brightness varies by about one magnitude and with a regular period. From the period-luminosity graph we estimate the absolute magnitude. Now log105.4 = 0.73 so apparent magnitude is -16. We then substitute into the distance formula:
m -M =510g~ => 16-(-3.5)=510g~ => d =3.2x104 parsecs 10 10
An open cluster is an irregular loose aggregation of a few hundred to a few thousand stars. They are clusters of young stars. Y is in the main sequence and so hydrogen is being fused into helium by the proton-proton chain or by the carbon cycle depending on their temperature. Region X is where red giants are found. These are large diameter very luminous stars. They have relatively cool surface temperature (-3000 K) which gives them a reddish colour. They 'burn' helium into carbon.
In main sequence stars hydrogen fuses into helium in its core. When the helium core reaches -12% ofthe star's mass it collapses and the increasing temperature causes the outer envelope to expand and cool to form a red giant. In the red giant helium fuses to form carbon in the triple alpha process. For stars of initial mass greater than -8 solar masses, the helium core fuses to form carbon and oxygen. When the helium is used up the carbon and oxygen combine to form neon, magnesium, sulfur and silicon. Later the silicon and sulfur form nickel and iron. Elements beyond iron are made by neutron capture during the cataclysmic explosion of a supernova.
A star commences its life in a cloud of extremely rarefied gas and dust. Some chance occurrence causes some aggregation of mass that leads to further attraction of mass. Gravitational potential energy is converted into heat and a protostar forms. Depending on its mass it may take tens of millions of years to reach the main sequence of the Hertzsprung-Russell diagram where its temperature is now high enough to cause the fusion of hydrogen into helium. Hydrogen burning continues for perhaps millions of years with a helium core forming. When this core reaches -12% of the mass of the star, the core contracts and the increased temperature causes the outer layers of the star to expand and cool forming a red giant. For stars of mass greater than -8 solar masses helium fusion now occurs forming carbon and oxygen. Further fusion takes place with the elements up to and including iron being synthesised. When the iron core mass approaches 1.4 solar masses the core collapses to a diameter of -20 km forming a neutron star and the outer layers are blown away in a violent supernova explosion. During this time the elements above iron are produced by neutron capture. If the collapsing core exceeds 3 solar masses the contraction continues until the core has a diameter of a few km - a black hole forms.
This is the 'turn-off' point where the star leaves the main sequence to form a red giant. Cluster M67 is the oldest cluster as it has the lowest turn-off point. This means that the older hotter stars (0, B and A) have evolved off the main sequence. This takes millions of years so the cluster must be old for it to have occurred.
Most of the alpha particles passed through the foil with only small deflections. About 1 in 8000 however, were deflected through angles greater than 90°. Rutherford interpreted these results and concluded that the only way for the heavy alpha particles to be deflected as they were, was if all of the positive charge of the atom and most of its mass was concentrated in a tiny core. He concluded also that the electrons would be around this nucleus and that most of the atom was empty space (allowing most alphas to pass through).
~=RH (~-~)=1.097X107 X(~-~)=2.44X106 -1 =:} /\'=410nm /\, n f n; 2 6
E =hf =h ~=6.626x10-34 x 3.0x108 =4.85x10-19 J /\, 410x10-9
Any two of the following: a Electrons can rotate in stationary states (energy states) without radiating energy. This was used to explain the stability of atoms. b When an electron falls from a higher energy state to a lower energy state the energy is quantised according to the Planck relationship t,E = hf. This was used to explain the line emission spectrum of hydrogen. c Angular momentum (mvr) is restricted to values
of ~. This was used to explain the existence of discrete energy levels. 2n
Bohr's model was unable to explain: why some aspects of classical physics worked and others did not; why it only worked for the lightest atom, hydrogen; the relative intensities of the emission lines; the presence of hyperfine spectral lines and the Zeeman effect - the splitting of spectral lines in a magnetic field.
The wave-particle duality is the recognition that matter exhibits some properties which we say are wave-like and others that we say are particle-like. Light had been demonstrated to have wave characteristics as had been shown by the fact that it exhibited the properties of interference and diffraction. It had also been shown to exhibit the photoelectric effect which could only be explained by assuming light was a particle. If this was true for light, de Broglie hypothesised it might also be true for other things that had previously only been considered to be particles such as electrons.
/\, =~ =~ =:} v =~ = 6.626x10-34
=9.10x105 m.s-1 p mv /\'m 8x10-10x9.1x10-31
Davisson and Germer fired a beam of electrons at a metallic crystal and looked at the intensity of the reflected electrons. They found the reflections to be consistent with diffraction patterns - the electrons were showing a wave characteristic.
de Broglie's hypothesis was that matter such as electrons showed wave characteristics and had a wavelength. If an integral number of wavelengths fitted exactly into the electron orbit, the wave would form a standing wave in which the energy was transformed between potential energy and kinetic energy but was not lost. This accounted for the stability of the atom.
Electron microscopes work in an analogous way to a light microscope except they use electron waves instead of light waves. The interior of the microscope is a vacuum which means only dead specimens can be examined. Magnetic lenses direct the electrons on to a very thin specimen and the different structures in the specimen absorb the electrons by different amounts. The electrons fall on a phosphor screen forming an image after focussing by a series of magnetic lenses.
The two most important qualities of any microscope are its magnification and its resolving power that is, its ability to distinguish small objects. The resolving power is limited by the wavelength used - the shorter the wavelength the better the resolution. Electron microscopes use shorter wavelength electron waves than the wavelength used by light microscopes giving -1000 times better resolution.
Chadwick believed that the penetrating radiation emitted from the beryllium after irradiation with alpha particles was the particle postulated by Rutherford to account for discrepancies in the mass of the nucleus. This particle was postulated to be neutral and so its detection was difficult. The paraffin block was rich in protons (lots of hydrogen atoms present) and collisions between the neutrons and protons caused the protons to be ejected and these could be detected because of their positive charge. By applying the laws of conservation of energy and momentum to these collisions, Chadwick was able to prove the existence of the neutron.
Isotopes were formed, many of which were radioactive.
~~Cu + 6n -7 ~~Cu then ~~Cu -7 ~~Zn + _?e Beta decay.
Any THREE of the following: neutrinos have no electric charge, no mass and no magnetic properties and would have hardly any interaction with matter. They would have energy, and momentum (linear and angular). During investigation of beta decay it was found that there was a discrepancy with the mass-defect of the emitted electron compared to the masses of the products and reactant (allowing for the massenergy relationship). Up to one-third of the energy that should have been associated with the electron was missing and nothing else could be found to account for the loss throwing the well established laws of conservation of mass, energy and momentum into chaos. Pauli's belief in these conservation laws led him to postulate that the neutrino was carrying away the missing energy. (The neutrino was not discovered until 26 years later.)
The nucleus 1jN has 7 protons and seven neutrons. Mass defect is the difference between the sum of the
masses of its nucleons and the mass of the nucleus, that is:
11m = [(7 x 1.007276) + (7 x 1.008665) -14.00307] = 0.108517 u
The binding energy can be found from the Einstein relationship E = mc2 and the fact that 1 u = 931 MeV. Binding energy = 101 MeV
In a controlled fission reaction only one neutron from each fission is available to split another nucleus -special materials in control rods absorb the extra neutrons. The result is a controlled rate of energy release. In uncontrolled reactions, each of the multiple neutrons released from the fission of one nucleus is allowed to hit another nucleus. The result is a rapid release of energy.
A thermal reactor is one which uses neutrons travelling at a speed comparable to the speed of gas molecules at room temperature. Enriched uranium is uranium in which the proportion of U-235 has been increased. U-235 is more readily fissionable with slow (thermal) neutrons than the more prevalent U-238. The moderator slows the neutrons down by colliding with the neutrons and absorbing some of their energy without absorbing the neutron itself. Moderator materials include ordinary and heavy water, graphite and beryllium. The control rods on the other hand absorb some of the neutrons without undergoing fission. By controlling the number of neutrons the rate of the fission reactions can be controlled. Control rods generally contain boron or cadmium.
Radioisotopes are radioactive isotopes that decay by releasing alpha, beta and/or gamma radiation. Radioisotopes can be artificially created by bombarding non-radioactive isotopes with neutrons. One industrial application of radioisotopes is in measuring wear in machinery. By placing radioisotopes
in the working parts of machines and measuring the radioactivity in the lubricating oil engineers can estimate the amount of wear. In medicine, radioisotopes can be used in isotopic scanning. The patient is given a radioisotope similar to an element used by the body, for example 1-131. This is taken up by specific organs (in this case the thyroid), and the distribution and abundance of the isotope can be detected by gamma cameras and any abnormalities can be found.
Neutrons are neutral - they have no charge. Neutrons have a wave-matter duality and so have a wavelength. Accordingly, they scatter - diffract - off matter. Whereas X-rays scatter best off high atomic mass atoms with lots of electrons, neutrons will scatter off hydrogen nuclei (protons) in hydrogen bonds found in all organic and most inorganic molecules. This makes the neutron scattering study of living material more effective than if using X-rays.
The Manhattan Project was the costliest engineering and scientific endeavour in its day. The successful production of the atomic bomb brought an end to the war against Japan in 1945. With it however, it also brought the start of the arms race and the Cold War. Rather than concentrating on eliminating disease and hunger in the world, massive amounts of money went into the manufacture of weapons of mass destruction. For decades the world lay in the grip of uncertainty with the threat of nuclear war always in the air. Some would argue that the MAD (mutually assured destruction) principle actually kept the world in relative peace, at least on a world scale. Others would argue that it cost the world the chance to eliminate war forever. Whatever view is held, it can be argued that the Manhattan Project had a significant impact on society.
Particle accelerators are devices used to accelerate subatomic particles to high speeds and hence high energies. The stability of the nucleus of atoms is determined by the value of the binding energy per nucleon. The higher this value, the more stable the nucleus. To break the nucleus up into its parts requires high energies - energies that can be produced only in particle accelerators. Because of the relationship between mass and energy given by E me2 it follows that the high mass exotic particles can only be observed after being 'created' in high-energy accelerators. Also the high energy means high speed and hence short de Broglie wavelength. This provides better resolution adding fine detail to observations. It follows that physicists require particle accelerators to investigate the structure of matter.
The standard model of matter is a theory that attempts to describe all interactions of subatomic particles (except those due to gravity). Its success lies in its ability to use a small number of particles and interactions to explain the existence of hundreds of particles and their interactions. The standard model has two main components to explain these forces: the electroweak theory which describes interactions through the electromagnetic and weak forces; and quantum chromodynamics which is the theory of the strong force. Physicists currently view matter as being grouped into three families - quarks, leptons and bosons. The standard model explains interactions in terms of these families, which it further classifies as matter particles - these are fundamental particles (that is, they have no known smaller parts) and are the quarks and leptons; and the force-carrier particles. Each type of fundamental force is caused by the exchange of force-carrier particles (also called messenger or exchange particles). These are the fundamental (or gauge) bosons. They include photons and gluons.
Cosmology is the study of the origin and evolution of the universe. Scientists believe that the universe began in the Big Bang some 15 billion years ago. From the 'cosmic egg' all matter formed. The laws of high-energy physics determine the ways in which this matter formed. Particles such as quarks 'sprang' into existence and these combined to make other particles. What happened in the first seconds and minutes after the Big Bang is speculative but relies on what is known about high-energy physics. Cosmology and high-energy physics are hence intimately joined.
E =_ GMm P r
a This is an example of projectile motion. The horizontal motion ofthe food package is constant velocity (with the velocity equal to that of the plane).
b From Newton's second law, as mass decreases, acceleration increases.
d
b
b The force between two parallel current carrying wires is given by f.- = k~ I d
1112 I I hence F =k d / xl=2xk _1_2 xl=2F
/2 d
d From Lenz's law the current will be induced in a direction so that its magnetic field will oppose the cause of the current that is, the end closest to the magnet will act as a south pole causing repulsion. The right hand grip rule shows the current to flow anticlockwise.
a A step-down transformer decreases voltage and increases current in the secondary relative to the primary. Power is constant.
c in a transformer, as voltage increases current decreases. The heating effect in conductors is proportional to the square of the current. Reducing the current reduces the heating losses.
a Most home appliances with motors have single phase induction motors. Three phase is used in industry.
d The shadow on the glass indicates the rays travel in straight lines.
a Ekmax
=hf -¢=hf -hfo =h(t -fo)=6.626x10-34(3.2-1.1)x1015 =1.39x1018 J
c The purpose behind doping is to increase the conductivity of semiconductors.
b
d The Meissner effect is the exclusion of a magnetic field by a superconductor.
1200 . 1200 Mass of astronaut = -- kg therefore weight on Mars = -- x 3.8 = 465.3 N
9.8 9.8 The safe re-entry of astronauts to Earth from space is restricted to a narrow 'window' in the Earth's atmosphere. The size of this window is determined by the need to prevent the spacecraft overheating and the need to keep the g-forces within safe limits. if the spacecraft attempts to enter the Earth's atmosphere at too shallow an angle it may 'bounce' off back into space (like a stone skipping across water). if it is too steep, the g-forces would be large enough to kill the occupants and the temperature generated would be too high for the spacecraft to withstand - it would burn up like a meteorite. it is found that an angle of 6.2±1° below the horizontal is the optimum to ensure safe re-entry. Special heat shields dissipate the intense heat produced even at this angle.
The time to hit the water is determined by the vertical motion which is constant acceleration.
1 12~y ~2X100 Hence ~y =-a yt 2 => t = /-- = --- =4.52s
2 ~ a y 9.8
The horizontal motion is constant velocity so the distance is given by: x = v xt = 10 x 4.52 = 45.2 m
A geostationary orbit is one with a period of 24 h in the plane of the equator. In one revolution with period T, the satellite travels a distance of 2rr:R where R is the radius of the orbit
. . 2nR 2nx42300x103 3
sospeedlsglvenbyv =--= =3.08x10 m.s-1
T 24x60x60 The acceleration due to gravity is equal to the centripetal acceleration at that height so
2 v2 (3.08x103
) 2 a = - = = 0.22 m.s-
R 42300 x 103
The stationary observer would determine a length contraction in the rod so we have:
I =/o~1_V2 =100 11_(0.95c i =31.2m (2 ~ (2
Because of time dilation the observer in the spacecraft would measure a time less than the stationary
t [-;2 I (0.95c i . observer that is: t = gO 2 :=} to =t~1--;T-2 =1x~1- 2 =0.312h=18mm43s
1-~ ( ( (2
It can be seen that the spaceship's crew ages less than their counterparts on Earth. This means it may be possible for the crew to reach distant planets in a 'reasonable' time from their reference frame although it would be much more time in the Earth's frame of reference. In this way travel to distant planets is theoretically possible (even if in reality it is not really feasible).
Electric motors utilise the motor effect - that is, a current-carrying conductor experiences a force in a magnetic field - to convert electrical energy into mechanical energy. Current is fed into the armature via the carbon brushes and this current sets up a magnetic field in the armature that interacts with the field of the permanent magnets or electromagnets. Application of the right-hand palm rule shows that the two sides of the armature experience forces in opposite directions (because the current flows in opposite directions). As a result the armature experiences a torque causing it to rotate (in an anticlockwise direction for the diagram shown). When the armature is in the vertical plane the split ring commutator reverses the direction of the current to ensure that a continuous rotation occurs. Any two of the following: use stronger magnetic fields; have more turns in the armature; use more current; have the pole pieces curved to produce a radial magnetic field; have more coils at angles to each other ...
A generator converts mechanical energy into electrical energy. By rotating the armature (coil) in the magnetic field we create a changing magnetic flux in the armature. By Faraday's law, an emf is induced in the coil and a current flows if there is a complete circuit. Carbon brushes, in contact with slip rings, take this current away. As the coil is rotated the rate of change of flux varies - it is biggest as the coil moves through the horizontal plane and least when it moves through the vertical plane. The direction of the current also changes as the coil rotates producing an AC voltage. The output voltage is shown in the diagram. Below it is the orientation of the coil at various times in the cycle. A split ring commutator would change the direction of the current each half cycle and convert the AC to DC. 2
Time
3 4 5
Eddy currents are circular currents induced in bulk conducting material situated in the presence of a changing magnetic flux. In an induction heater, coils are placed under a ceramic cook top and alternating currents in the coils induce currents in the metal cookware placed above them. These eddy currents flowing in the metal heat it and its contents, cooking the food. In electromagnetic braking, a metal sheet or wheel is brought near to a strong magnet (either permanent or produced by current-carrying coils). Induced eddy currents flow in a direction to oppose their cause (Lenz's law) and this brings the wheel to rest. This braking is used in some modern trains and in some fun-park rides.
A transformer consists of two conducting coils - a primary coil and a secondary coil- wrapped around the same soft iron core. Alternating voltages connected to the primary coil cause a changing magnetic flux in the iron core. This changing flux induces a changing emfin the secondary coil. By having different number of turns in the primary and secondary the voltage can be changed. If the secondary has more turns than the primary, the voltage in the secondary is bigger than the voltage in the primary -a step-up transformer. The voltage supplied to homes is 240 V. Many home appliances require smaller voltages (or larger in some cases such as in televisions) to operate. Transformers inside the various appliances produce the required voltages.
In an AC induction motor, a rotating magnetic field is set up in the stator which induces currents in the rotor (by electromagnetic induction). These currents produce a magnetic field that interacts with the stator's field. The result is that the stator's magnetic field 'drags' the rotor around. Any two of the following: they are cheap, reliable, efficient.
Thomson arranged the electric and magnetic fields in such a way that the deflections cancelled each other, allowing the electrons to travel straight through. That is Felectric = Fmagnetic' When the forces are
£ balanced q£ =qvB => v =-. Thomson could measure £ and B and so he could calculate v.
B
% 20,% The electric field can be found from £ = V so v = ~ = 0.01 = 2 x 107 m.s-1
d B 0.001 The force on the electron due to the magnetic field is given by
F =qvB =1.602x10-19 x2.0x107 xO.001=3.2x10-15 N
The electron gun produces the beam of electrons and accelerates them towards the fluorescent screen. Cathode ray oscilloscope. TVs use magnetic fields to control the path of the electron beam.
Solar cells come in several forms but they essentially consist of two different conducting materials in contact with each other - these can be a metal and a semiconductor or two oppositely doped semiconductors. Consider a simple p-n junction. Electrons initially drift from the n-type material (where they are the majority charge carriers) into the p-type material, and holes diffuse from the p-type into the n-type. The result is that the n-type material near the junction is positive (electrons have been lost) and the p-type is negative (electrons have been gained). An electric field is set up that opposes further diffusion of charge carriers. However, light falling on the semiconductor creates electron-hole pairs by means of the photoelectric effect. The free electrons are attracted to the n-type and travel through an external circuit and the holes move to the p-type - an electric current is the result. The current depends on the rate of creation of the electron-hole pairs which in turn depends on the light intensity. In this way, solar cells convert light energy into electrical energy.
The Braggs used X-rays to investigate the structure of crystals. They were able to determine the arrangement of atoms and their interatomic spacing. They bombarded crystals with X-rays and detected the scattered X-rays. They found that the atoms
were arranged in a regular pattern in the crystal and they discovered a relationship that allowed them to determine the spacing or the wavelength (depending on which one was already known).
Superconductivity is the elimination of electrical resistance in certain materials at very low temperatures. As the temperature of a conductor such as a metal is reduced the resistance decreases in a non-linear manner. At a very low temperature called the transition temperature, the resistance ceases altogether. This temperature varies from material to material. For mercury, the first superconductorto be discovered, this temperature is -4.2 K. Anyone of the following: Present day uses include 1. Magnetic Resonance Imaging (MRI) machines where superconducting coils produce the intense magnetic fields required in MRI scanning - these coils allow currents to flow with little energy loss. 2. Magnetic levitation - superconductors produce the intense magnetic fields used to lift experimental Maglevtrains offthe tracks to reduce friction. 3. SQUIDS - Superconducting quantum interference devices use the Josephson effect to detect minute magnetic field variations. Future uses include: 1 Superfast computers using superconducting switches; Electricity transmission - if superconducting materials can be used to transmit electricity, energy losses could be significantly reduced. The very low temperatures required are preventing their widespread use today.
Ultrasound is: non-invasive, relatively cheap, portable, has no side effects, does not use radiation. The acoustic impedance of air and skin are vastly different. This would result in almost all the ultrasound being reflected from the air/skin interface. Since ultrasound imaging requires energy to be transmitted through the patient's skin a coupling medium is used. The Doppler effect is the apparent change in frequency when there is relative motion between a source of sound (or any wave) and an observer.
ii In Doppler echocardiography, ultrasound is reflected off moving blood cells and/or moving heart valves. The resulting frequency change indicates the speed of the blood flow which tells the doctor about the functioning of the circulatory system, particularly the heart. The acoustic impedance is a measure of the ease with which a material transmits ultrasound.
Ir [Z2-Z,]2 [(1.62-1.38)X106t
-= = =0.0064 122
o [Z2+Z'] [(1.62+1.38)x106]
The small amount of reflection (0.64%) means that the fat and kidney will be difficult to differentiate between. Electron-positron annihilation occurs when an electron collides with a positron and their massenergy is converted into two gamma rays that travel in opposite directions; +~e + _~e ~ 2y
The electrons come from tissue in the patient; the positron comes from a radiopharmaceutical. A radiopharmaceutical is a bio-molecule commonly used by the human body which has a positron emitting radioactive atom substituted for a normal atom. This is given tothe patient and is selectively taken up by the organs in the body that is being scanned. PET has the advantage that it shows organ function as well as organ structure.
The most appropriate imaging techniques for the particular medical condition are: fractures - simple radiograph; foetal development - ultrasound; stroke - magnetic resonance imaging. A simple radiograph will uncover a bone fracture easily and relatively cheaply. Ultrasound has no ionising radiation and no known side effects - characteristics essential in ensuring the safety of a developing foetus. MRI is the scanning technique of choice for the brain and central nervous system because of its ability to easily distinguish between white and grey matter in the brain and spinal cord.
Anyone ofthe following: 1. Selective absorption of various components of the electromagnetic spectrum by the atmosphere. This can be overcome by placing the telescopes in orbit (for example, the Hubble Space Telescope) 2. The problem of 'seeing' -the effect of looking through great depths of atmosphere causing distortion of the image. This can be minimised by: placing the telescope in orbit; situating the telescopes on high mountaintops; using adaptive optics. 3. Poor resolution -the inabilityto distinguish between two close objects. This can be improved by using an interferometer. Bigger telescopes have better light-gathering power (sensitivity) because of the larger area of the dish and better resolving power (resolution) because of the larger diameter. Apparent magnitude is the magnitude as viewed from Earth. Absolute magnitude is the magnitude the star would have if it were placed 10 pc from Earth. The fact that the magnitudes are different simply reflects the fact that Canopus is not 10 pc from us. Spectra can be classified according to criteria such as temperature. This in turn determines the strength of the hydrogen absorption lines and the presence or absence of other spectral lines. For example, stars with strong helium ion lines are spectral class 0; the darkest hydrogen absorption lines belong to spectral class A; stars with prominent titanium oxide lines are spectral class M. Other classes have different spectral lines. In spectroscopic parallax, the spectral class and luminosity can be used to estimate the absolute magnitude. From the Hertzsprung-Russell diagram the apparent magnitude can be estimated. Substitution into the appropriate distance formula allows the distance to be calculated.
Hadar is hottest as it is a B1 star and the scale goes 0, B, A, ... , M with 0 the hottest followed by B, A, ... Arcturus is orange as it belongs to the K2 spectral class.
iii Hadar is the faintest star because it has the largest apparent magnitude (as magnitude increases, brightness decreases).
d d d m -M =510g
lO => loglO=0.63-(-5.2) => loglO=1.166 => d =147pc
An astrometric binary is one where only one star is visible. The existence of the other star in deduced from its effect on the orbit of the visible star. Anyone of the following: Visual binary - both stars are visible orbiting around their common centre of mass; spectroscopic binary - recognised by the periodic doubling of the spectral lines; eclipsing binary - recognised by the periodic variation in the light intensity as one star eclipses the other.
The more massive a star the faster it evolves. The greater the mass, the faster the protostar reaches temperatures high enough to initiate nuclear fusion reactions and the further to the upper left-hand side it joins the main sequence ofthe Hertzsprung-Russell diagram. It may take a star of -1 solar mass millions of years to reach the main sequence but only a few hundred thousand years for a star of -10 solar masses. Bigger mass stars use their fuel at a faster rate than smaller mass stars - the increased rate is greater than the increase in fuel supply. This occurs because the large star needs to burn its fuel faster to counteract the larger gravitational pull. Consequently the star spends less time on the main sequence than lower mass stars and evolves faster into red giants, neutron stars, black holes ...
The Bohr model of the atom has the electrons revolving in discrete energy levels around the nucleus. When an electron falls from a higher energy level to a lower energy level it gives-off a photon with energy given by E = hf. For example, the transition between the third energy level to the first energy level can be done in three ways: directly from n = 3 to n =1 or from n 3 to n = 2 and then n = 2 to n = 1. It follows that the frequency from level 3 to 1 is the sum of the frequencies from level 3 to 2 and level 2 to 1.
The ground state is the lowest energy level, corresponding to n = 1.
The required energy is given by E =hf =h ~ . The wavelength is found from the Balmer equation
.2. =R H (~---;-)= 1.097 X107 X(~-~)=9.75 x106 m-1
A n f ni 1 3
50 E =h -i=hC X±=6.626X10-34 x3.0x108 x9.75x106 =1.94x10-18 J
de Broglie postulated that matter existed as both waves and as particles -the wave-particle duality. Davisson and Germer bombarded a nickel crystal with electrons. The electrons scattered off the crystal in a manner consistent with the electrons being diffracted - the electrons were acting as waves.
Heisenberg is remembered for introducing a mathematical theory of quantum mechanics using matrices. This was found to be equivalent to the model proposed by 5chr6dinger. Heisenberg also proposed the uncertainty principle that said that the more we know about an elementary particle's position, the less we know about its subsequent history this was the end of deterministic physics. Pauli is remembered for the formulation of the exclusion principle that explained the periodicity of the elements. He also predicted the existence of the neutrino.
A radioisotope is a radioactive isotope. The relatively short half-life means that it lasts long enough to do its job in scanning but short enough that it does not cause damage to the surrounding tissues.
The fuel is generally of enriched uranium containing a greater proportion of U-235 than found in natural uranium. The U-235 undergoes fission when bombarded with thermal neutrons, releasing energy along with additional neutrons that can be used to continue the reaction. The moderator slows down the neutrons to thermal energies, as they are more likely to cause fission than the faster neutrons. The control rods absorb excess neutrons to control the reaction rate. Too many neutrons and an uncontrolled chain reaction will occur. The radiation shielding protects the personnel from the radiation and the reactor walls from damage.
Quarks and leptons. Combinations of quarks make up protons, neutrons and mesons. Leptons include electrons, neutrinos and muons. Anyone of the following: photon - mediates the electromagnetic force; gluon - mediates the strong nuclear force; weakon - mediates the weak nuclear force; graviton (not yet detected) hypothesised to mediate the gravitational force.
( = fA
I . 1 ntenslty oc-
d 2
V 1 sin i -=--
E=~ q
R=~ I
P = VI
Energy = VIt
ilv v - u a =-=--av ilt t
"LF = ma
E 1 2 k = 2mv
p = mv
ilp = Ft
F = Gm 1m 2
( 2
(3 GM -T2 4n-2
4n-2( 3 m 1+m2=-
GT 2
M =m -5109(10)
d=~ p
F =BII sinS
~=kI1I2 l d
r=Fd
r=nBIA cosS
E =-G m 1m2 p (
t g 2
1-(2
F = qvB sinS
E = ~ d
E = hf
Z =pv
Ir [Z 2 -Z i -= Ia [Z 2 +Z It
~=RH(_1 __ 1 ) A n/ n/ A=~
mv
Numerical values of several constants
Charge on the electron, qe
Mass of the electron, me
Mass of neutron, mn
Mass of proton, mp
Speed of sound in air
Earth's gravitational acceleration, 9
Speed of light (in vacuum), C
Magnetic force constant (k = ~ )
Universal gravitational constant, G
Mass of Earth
Planck's constant
Rydberg's constant, RH
Atomic mass unit, U
1 eV
Density of water, p
Specific heat capacity of water
-1.602 x 10-19 C
9.109 X 10-31 kg
1.675 x 10-27 kg
1.673 x 10-27 kg
340 m.s-1
9.8 m.s-2
3.00 x 108 m.s-1
2 x 10-7 N.A-2
6.67 x 10-11 N.m2.kg-2
5.983 x 1024 kg
6.626 x 10-34 J.s
1.097 x 107 m-1
1.661 X 10-27 kg 931.5 MeV/c2
1.602 X 10-19 J
1.00 x 103 kg.m-3
4.18 x 103 J.kg-1.K-'
A A-scan 54 absorption spectra 77-78 AC electric motors 35 AC generators 27-28 AC voltages 31-32 acceleration 2-6 acoustic impedance 54-55 adaptive optics 71 alpha rays 62, 105 angular momentum 66, 95 anodes 38-39, 58 astrometric binaries 87 astrometry 74 atomic models 46-50, 94-95 atomic number 105
B 8-scan 54 Balmer formula 94-95 band structure 46 BCS model of superconductors 51 beta rays 62, 105 binary stars 86 binding energy 106, 114 black body radiation 42, 79 black hole 91 Bohr model 95-99 bosons 114-115 brightness of stars 82, 86-87
C cathodes 38-39, 58 cathode rays 38-39 centripetal acceleration 5-6 Cepheid variables 87 chain reactions 106-107 charge to mass ratio 39 charges moving 19, 39 clusters of stars 90-91 colours of stars 83,90-91 communication with satellites
10-11 commutators 19-20, 27 computerised axial tomography
CAT 58 conduction electricity 19, 46-47 conservation of energy 23,31,
105-106 conservation of momentum 10,
105-106 Cooper pair 51 crystal structure 50 current 19-20, 31
o DC electric motors 19-20 diffraction pattern 98 distance to galaxies 83, 87 doping semiconductors 46-47 Doppler effect 55, 86 drift velocity 50
E Einstein 14-15,43 electric field 39 electric generators 27-28 electric motors 19-20
electricity 27-32 conduction in metals 50
electromagnetic induction 23-28 electromagnetic radiation 10-11,
42-43, 58-59 electromagnetic spectrum 70,
77-79 electron(s} 42-43, 102
atoms 46-51, 94-98 electron diffraction 98 electron microscopes 39, 102 emf24-31 emission of electrons 42-43 emission spectra 77, 94-95 endoscope 59 energy, conservation 23, 31,
105-106 energy levels atoms 46,77-78,95 energy, binding 106 escape velocity 5 ether 14 evolution of stars 90-91
F Faraday's law 23-27 fibre optics 59 force(s} 2, 6, 19-20
charge in magneticfield 19, 39 force-carrier particles 114-115 frame of reference 14-15 frequencies 77-78
G g 2-7 galaxies 87 gamma rays 62-63, 105 generators 27-28 geostationary orbit 6 germanium 46-47 gravitational potential energy 2, 90 gravity 2-7
H half-life 62 Hertzsprung-Russell diagram 83,
90-91 Hipparcos 74 holes, conduction 46-47 hydrogen in stars 91 spectrum 94-95
induction cookers 24 induction motor 35 inertial frame of reference 14-15 insulators 46 interference 71, 98 inverse square law 10 isotopes 62-63, 105-110
K, L Kepler's laws 6 length contraction 15 Lenz's law 23-24leptons 114-115 light 14,43 light-years 74 line emission spectra 77, 94-95 luminosity of stars 82, 87-91
M Maglev train 51 magnetic fields 19-32, 39, 66-67 superconductors 51
magnetic flux/induction 23-32 magnetic lenses 102 magnetic resonance imaging
MRI 51, 66-67 magnitude of stars 82-83, 90-91 main sequence stars 90-91 Manhattan Project 111 mass defect 106 mass number 105 matter particles 114-115 Meissner effect 51 metals structure 50 Michelson-Morley experiment 14 momentum 66, 95 conservation 10, 105-106
motor effect 19-20
N n-type semiconductors 47 neutrino 99, 105-106 neutron star 91 neutrons 66, 105-107, 111, 115 Newton's law of gravity 2, 86 nuclear fission 106-110 nuclear force 106, 114-115 nuclear reactions in stars 91 nucleons 105,114 nucleus 94, 105
O,P optics of telescopes 70-71 p-type semiconductors 47 pair annihilation 63 parailiax 74, 83 parsecs 74 particle accelerators 114 period-luminosity relationship 87 phase scan 54 photoelectric effect 42-43, 98 photometry of stars 82-83 photons 43, 77-79, 115 piezoelectric crystals 54-55 Planck equation 42-43, 77, 95 positron emission tomography
PET 63 potential energy 2 power 31-32 power lines 28-32 projectile motion 5 protons 66, 105, 115 protostar 91
Q, R quantum theory 42-43, 95 quarks 114-115 radioactivity 61-62, 105-107 radioisotopes 62-63, 110 re-entry of spacecraft 7 red giants 90-91 red-shifted spectra 78 reference frame 14-15 relativity, special 14-15 resistance in superconductors
50-51 resolution of telescope 70-71
right-hand palm rule 19-24 rockets 5-10 Rutherford model 94
S satellites 5-6, 74 sector scan 54-55 semiconductors 46-47 sensitivity of telescope 70-71 silicon 46-47 simultaneity 15 solid state devices 46-47 spacecraft 5-11 special relativity 14-15 spectroscopic parallax 83 spectra 94-95
stars 77-79, 86 spin of particles 66 standard model of matter 114-115 stars
brightness 82-91 classes 78, 90 clusters 90-91 colours 83, 90-91 evolution 90-91 spectroscopy 77-79, 83
Stefan-Boltzmann law 79 stellar see stars sunspots 10 superconductors 50-51 supernova 91
T telescopes 70-71 television 39 temperature of stars 79, 90-91 thermionic emission 47 time dilation 15 torque 19-20, 35 trajectories 5-7 transformers 31-32 transistors 47 transition temperature 51 transmutation 105 trigonometric parallax 74 twin paradox 15
U ultrasound 54-55 uncertaintiy principle 99 uranium 106-110
V valence band 46 Van Allen radiation belts 10-11, 19 variable stars 87 velocity 5-6, 14 voltage 27, 31-32
W,X,Z wave nature electrons 39 wave particle duality 98 wavelength 70, 77-79 weight 2 white dwarfs 90-91 work 2 X-rays 58-59 X-ray crystallography 50-51 2eeman effect 95
When doing an examination the following process should be used: 1 Read the question twice 2 Underline key words' :3 Work out what the question is after 4 Plan, then write your answer 5 Read through your answer and check for errors and/or omissions.
The examination is worth 100 marks and you have three hours (180 minutes) to complete it. It follows that each mark is 'worth' 1.8 minutes (1 min 48 s) of your time. Keep this in mind as you do different questions with a range of marks. For example you should spend about 18 minutes on a 10 mark question but only about 9 minutes on a 5 mark question. Some flexibility is OK but remember that if you use too much time on one question it will affect the amount of time you have to complete the remaining questions.
You are allowed 5 minutes reading time, in addition to the 3 hours to complete the exam. During this time you are not allowed to write but should skim through the paper to find the 'easier' questions. These should be done before the harder questions. Success with these easier questions will set you up for a good result and give you the confidence to attack the harder questions.
Multiple Choice - Section I Part A of the paper is multiple choice. Multiple choice questions have four alternatives to choose from: A, B, Cor D. These include the correct answer and three distractors. These distractors are chosen to divert you from the correct answer by providing plausible answers or answers that contain common mistakes or misconceptions by students. Often one of two of the distractors can be eliminated easily but the other two may appear to be possible. This is where your deeper knowledge and understanding is required. If you cannot separate them, go with your 'gut feeling'. Do not leave the answer blank. Practise with this style of question makes 'perfect'. Extended Response Questions - Section I Part B of the paper is composed of extended response (also called free response) questions. They contain a range of marks and relate to the Core topics: Space; Motors and Generators and From Ideas to Implementation. Some of the questions are in parts such as (a), (b), (c) .. , and some ofthese may be further divided into additional parts (a) (i), (a) (i0 ... The marks give an indication of how much information you need to provide. The more marks there are, the more points or arguments you need to write. For example a two mark question may require two points; a three mark question may require three points. Key words give an indication of the difficulty of the question. Questions that commence with 'State' are generally easier than those that begin with 'Justify' or 'Evaluate'. Some questions ask for a more integrated approach. These are the ones that are not divided into parts but ask you to justify, compare and contrast, discuss ... Choose the most appropriate form of response. It does not have to be in prose; tables, diagrams and flowcharts may be suitable. For quantitative questions, that is, those requiring a mathematical calculation, it is important that you show your working. You may receive marks for a partly correct answer. Add units to all numerical answers (if applicable). Option Topics -In Section II, answer questions from ONE option only. Like the extended response question in Section I Part B, questions will have parts that correspond to different areas of the topic content. Some of these may be further divided or require a more integrated approach. Remember to read the question twice, underline the key words, plan your response and then write your answer. Read your answer and look for mistakes and/or omissions. As for Part B, for quantitative questions, it is important that you show your working. Attempt all questions. You do not get penalised for incorrect answers but you cannot get a mark for a blank space! Exam Reports - Using the board's website, you can obtain copies of Physics Examination Reports. From these you can find the common mistakes and misunderstandings of students. Learn from these! , There are a number of key words that may be obtained from the Science Syllabus Support Document on the Board of Studies website at
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