success one hsc physics

Free-to-download HSC Exam with answers

Past HSC Questions & Answers2001–2003 by Topic2005–2013 by Paper

SUCCESS ONE ®

HSC*

PHYSICS

Physics

4000

2012H I G H E R S C H O O L C E R T I F I C AT E

E X A M I N AT I O N

General Instructions

• Reading time – 5 minutes

• Working time – 3 hours

• Write using black or blue penBlack pen is preferred

• Draw diagrams using pencil

• Board-approved calculators maybe used

• A data sheet, formulae sheets andPeriodic Table are provided atthe back of this paper

• Write your Centre Number andStudent Number at the top ofpages 13, 17, 19, 23, 25 and 27

Total marks – 100

Pages 2–28

75 marks

This section has two parts, Part A and Part B

Part A – 20 marks

• Attempt Questions 1–20

• Allow about 35 minutes for this part

Part B – 55 marks

• Attempt Questions 21–30

• Allow about 1 hour and 40 minutes for this part

Pages 29–39

25 marks

• Attempt ONE question from Questions 31–35

• Allow about 45 minutes for this section

Section II

Section I

433

2 0 1 2 H S C E X A M I N A T I O N P A P E R • Q U E S T I O N S

Exce l S U C C E S S O N E H S C • P H Y S I C S

C H A P T E R 1 4

where required

9781741254730 SuccessOne PHYSICS 2014Ed.indb 4339781741254730 SuccessOne PHYSICS 2014Ed.indb 433 11/12/13 11:36 AM11/12/13 11:36 AM11/12/13 11:36 AM

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Section I75 marks

Part A – 20 marksAttempt Questions 1–20Allow about 35 minutes for this part

Use the multiple-choice answer sheet for Questions 1–20.

1 The diagram shows a device connected to a meter.

What device is shown in the diagram?

(A) AC motor

(B) DC motor

(C) AC generator

(D) DC generator

2 What is currently used to define the standard metre?

(A) The speed of light

(B) The signals from GPS satellites

(C) The wavelength of light from a krypton lamp

(D) The distance between two lines on a platinum iridium bar

N S

Meter

0 2

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C H A P T E R 1 4 • 2 0 1 2 H S C E X A M I N A T I O N P A P E R


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3 What part of a cathode ray tube allows a person to observe the position of an electronbeam?

(A) A maltese cross

(B) A heated filament

(C) A fluorescent screen

(D) A uniform magnetic field

4 The graph shows how the gravitational potential energy (Ep) of a satellite changes withits altitude.

What is the change in gravitational potential energy of the satellite when its altitude isreduced from 14 000 km to 4000 km?

(A) –8.8 × 109 J

(B) –2.8 × 109 J

(C) 2.8 × 109 J

(D) 8.8 × 109 J

–10

Altitude (km)

Ep

(109

J)

–9

–8

–7

–6

–5

–4

–3

–2

–1

00 5000 10 000 15 000 20 000

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5 Which of the following could be added to a crystal of silicon to create a p-typesemiconductor?

(A) Carbon

(B) Copper

(C) Gallium

(D) Phosphorus

6 The diagram represents the electric field around a negative charge.

If the magnitude of the charge were doubled, which diagram would best represent thenew electric field?

–

–2

–2

–2

(A) (B)

(C) (D)

–2

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7 In moving-coil galvanometers, the coil experiences a torque because of the currentflowing through it.

What ensures that this torque is directly proportional to the current flowing through thecoil?

(A) A return spring

(B) A radial magnetic field

(C) A laminated soft iron core

(D) A constant cross-sectional area of the coil

8 A current-carrying wire passes through a region of uniform magnetic field, magnitude0.05 T, and as a result experiences a force of magnitude 0.03 N.

What is the current I?

(A) 1.5 A

(B) 1.7 A

(C) 3.0 A

(D) 6.0 A

9 Compared to a geostationary orbit, which row of the table correctly describes the relativeproperties of a low Earth orbit?

30°

B

0.2 m

I

Orbital velocity Orbital period

Higher Higher

Higher Lower

Lower Higher

Lower Lower

(A)

(B)

(C)

(D)

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10 Which of the following ideal transformers could be used to convert an input voltage of20 volts AC to an output voltage of 2 volts AC?

11 Which of the following is correct about the forces acting during a rocket launch?

(A) Equal and opposite forces act on the rocket. This enables it to continue to accelerateeven in the vacuum of space.

(B) The engines exert an upward thrust on the rocket. This thrust exceeds thedownward force of the engines on the air.

(C) The rocket engines exert a downward force on the gases being expelled. Thesegases exert an upward force on the engines.

(D) The expelled gases exert a force against the launch pad. The launch pad then exertsan equal and opposite force on the rocket causing it to accelerate.

(A) (B)

(C) (D)

4 turns 10 turns 20 turns 3 turns

20 turns 10 turns 3 turns 30 turns

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Use the data below to answer Questions 12 and 13.

12 What is the centripetal force experienced by the Moon due to Earth’s influence?

(A) 2.0 × 1020 N

(B) 1.6 × 1022 N

(C) 4.7 × 1026 N

(D) 7.6 × 1028 N

13 What is the orbital period of an Earth satellite having an orbital radius half that of theMoon?

(A) 5.9 × 105 s

(B) 8.3 × 105 s

(C) 1.2 × 106 s

(D) 7.5 × 106 s

Orbital period of the Moon around Earth 2.36 × 106 s

Mean orbital radius of the Moon 3.83 × 108 m

Mass of Earth 6.0 × 1024 kg

Mass of the Moon 7.35 × 1022 kg

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14 The graph shows variation in magnetic flux through a coil with time.

Which graph best represents the corresponding induced emf in the coil?

15 A magnet can be levitated above a superconductor, when the superconductor is below itscritical temperature.

Which statement best describes how this occurs?

(A) All of the magnet’s field is absorbed by the superconductor.

(B) The superconductor creates currents in the magnet, resulting in a repulsive force.

(C) Cooper pairs are exchanged between the superconductor and the magnet throughits field.

(D) Some of the magnet’s field is excluded by the superconductor, resulting in arepulsive force.

Time

Magneticflux

Time

Inducedemf

(A)

Time

Inducedemf

(B)

Time

Inducedemf

(C)

Time

Inducedemf

(D)

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16 An ideal electric motor connected to a DC voltage source rotates at a constant rate of200 revolutions per minute. There is no load on the motor.

Which of the following is a correct statement about the operation of the motor?

(A) The applied voltage must exceed the back emf in order to keep the motor running.

(B) There is no back emf because it is only produced in AC motors due to the changingflux.

(C) The back emf is equal to the applied voltage because no work is being done by themotor.

(D) The back emf must exceed the applied voltage to prevent the motor’s speed fromincreasing.

17 The following equipment is attached to a DC power supply.

What current must be flowing through the wires to result in a force of 2.50 × 10–3 Nbetween them?

(A) 0.224 A

(B) 5.00 A

(C) 12.5 A

(D) 25.0 A

2.00 mm2.00 mm 1.00 m

Copper wires

– +

Liquid conductor

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18 The gravitational force, due to Earth, on a mass positioned at X is Fx and on the samemass positioned at Y is Fy. The diagram is drawn to scale.

What is the value of ?

(A) 1.5

(B) 2.0

(C) 2.25

(D) 4.0

19 The diagram represents an induction cooking system.

Which row in the following table shows the set of conditions that would result in the mostrapid heating of the base of the cooking pot?

AC voltage frequency Electrical resistance of pot base

Low Low

Low High

High Low

High High

(A)

(B)

(C)

(D)

Base of the cooking pot

Ceramic cooktop

AC voltage source

Earth

X Y THIS DIAGRAM ISDRAWN TO SCALE

F

Fx

y

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20 A company wishes to develop a semiconductor sensor to detect thermal radiation frompeople. The sensor will work on the same principle as a solar cell.

Using the information provided, which semiconductor would be most suitable for thispurpose?

(A) HgCdTe

(B) InSb

(C) Si

(D) GaN

Inte

nsity

10 20

Wavelength (mm)

Typical Human Blackbody Radiation Curve

Semiconductor Band gap (eV)

HgCdTe 0.03

InSb 0.17

Si 1.1

GaN 3.4

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2012 HIGHER SCHOOL CERTIFICATE EXAMINATION

Physics

Section I (continued)

Part B – 55 marksAttempt Questions 21–30Allow about 1 hour and 40 minutes for this part

Answer the questions in the spaces provided. These spaces provide guidance for the expectedlength of response.

Show all relevant working in questions involving calculations.

Question 21 (6 marks)

(a) Outline a first-hand investigation that could be performed to measure a value foracceleration due to gravity.

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(b) How would you assess the accuracy of the result of the investigation?

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(c) How would you increase the reliability of the data collected?

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(d) How would you assess the reliability of the data collected?

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A bar magnet is placed on a sensitive electronic balance as shown in the diagram. Ahollow solenoid is held stationary, such that the magnet is partly within the solenoid.

The solenoid is then lifted straight up without touching the magnet. The reading onthe balance is observed to change briefly.

(a) Why does a current flow in the solenoid?

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(b) Explain the reason for changes in the reading on the electronic balance as thesolenoid is removed.

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N

Solenoid Copper wireshort circuit

Bar magnet

Electronic balanceS

42.42 g

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Consider the following thought experiment.

Two towers are built on Earth’s surface. The height of each of the towers is equal tothe altitude of a satellite in geostationary orbit about Earth. Tower A is built at Earth’sNorth Pole and Tower B is built at the equator.

Identical masses are simultaneously released from rest from the top of each tower.Explain the motion of each of the masses after their release.

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Tower B

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Physics

Section I – Part B (continued)


(a) Using a labelled diagram, outline the differences in the energy bands ofconductors, semiconductors and insulators.

(b) Explain why a current is able to flow in a pure semiconductor when an electricfield is applied across it.

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Physics



(a) Why have transistor circuits largely replaced thermionic devices?

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(b) Assess the impact of the use of transistors on society.

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A transmission line is to be used to supply 100 MW of power from a power station toa substation 100 km away. Three possible designs are shown below.

Question 26 continues on page 21

Power station120 MW

output

Substation100 MW input

33 kV input

Design A – Low voltage

100 km

Power stationwith step-uptransformer,

508 kV output

Design B – High voltage

40 W totalline resistance

Substation100 MW input500 kV input

100 km

100 km

Powerstation

Substation100 MW input

Design C – Superconducting

Superconductingtransmission line

The cooling requirements for the superconducting transmission line consume 30 kW per km of line

Question 26 continues

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Question 26 (continued)

Using physics principles and appropriate calculations, evaluate each design to determinethe best way of transmitting power from the power station to the substation.

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End of Question 26

6

End of Question 26

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Physics



A toy bird is launched at 60° to the horizontal, from a point 45 m away from the baseof a cliff.

Calculate the magnitude of the required launch velocity such that the toy bird strikesthe base of the wooden building at the top of the cliff, 34 m above the launch height.

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Physics



(a) Outline ONE piece of evidence supporting Einstein’s theory of relativity.

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(b) What criteria are used to test and validate a theory?

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(c) The distance between the cathode and screen in a cathode ray tube is 40 cm.

If an electron travels through the tube at 3.0 × 107 m s–1, what is the apparentdistance from the cathode to the screen in the electron’s frame of reference?

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Physics



How is the motor effect used to produce different sounds in a loudspeaker? Include alabelled diagram.

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The diagram shows the paths taken by two moving charged particles when they entera region of uniform magnetic field.

(a) Why do the paths curve in different directions?

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(b) Why are the paths circular?

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Path P

Path Q

B = 1.0 T

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Physics

Section II

25 marksAttempt ONE question from Questions 31–35Allow about 45 minutes for this section

For Questions 31–34• answer parts (a)–(c) of the question in Section II Answer Booklet 1.• answer parts (d)–(e) of the question in Section II Answer Booklet 2.Extra writing booklets are available.

For Question 35• answer parts (a)–(b) of the question in Section II Answer Booklet 1.• answer parts (c)–(d) of the question in Section II Answer Booklet 2.Extra writing booklets are available.

Show all relevant working in questions involving calculations.

Pages

Question 31 Geophysics ........................................................................... 31–33

Question 32 Medical Physics ......................................................................... 34

Question 33 Astrophysics ......................................................................... 35–36

Question 34 From Quanta to Quarks ............................................................. 37

Question 35 The Age of Silicon ............................................................... 38–39

(Not included in this reproduction)

(Not included in this reproduction)

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Question 32 — Medical Physics (25 marks)

Answer parts (a)–(c) in Section II Answer Booklet 1.

(a) (i) The first X-ray image of a human was made in 1895 but it was not until1972 that CAT scan imaging was developed.

Account for the time interval between the development of these tworelated technologies.

(ii) Contrast the information provided by PET scans and CAT scans.

(iii) Contrast the production of radiation used for PET scans and CAT scans.

(b) (i) What effects do the pulses of radio waves have on hydrogen nuclei in thebody of a person having a magnetic resonance image scan?

(ii) Outline how advances in physics in the 20th century contributed to thedevelopment of magnetic resonance imaging.

(c) Describe the properties that make a radioactive isotope useful for medicalimaging. Include a specific example of a radioactive isotope in your answer.

Answer parts (d)–(e) in Section II Answer Booklet 2.

(d) Explain how endoscopes obtain images of internal organs.

(e) Discuss the range of information obtained from, and the limitations of,ultrasound medical imaging technology.

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Question 33 — Astrophysics (25 marks)


(a) (i) Why do astronomers use both apparent and absolute measurements inphotometry?

(ii) Compare how astronomers obtain photometric and spectroscopic data.

(b) (i) Describe the problems associated with ground-based optical astronomyin terms of resolution.

(ii) How can the resolution of ground-based optical telescopes be improved?

(c) (i) Draw a flow diagram for stellar evolution using the following celestialobjects:

• Black hole

• Main sequence star

• Neutron star/pulsar

• Planetary nebula

• Red giant

• Supernova

• White dwarf.

(ii) All naturally occurring elements have been synthesised within stars.Explain how this occurs.


(d) (i) Explain how trigonometric parallax is used to determine the distances tostars.

(ii) Outline ONE limitation of using trigonometric parallax to determinedistances to stars.

Question 33 continues on page 36

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Question 33 continues

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Question 33 (continued)

(e) Astronomers have obtained the following data about stars in a binary system.

Analyse the above data to write a detailed description of this binary system.

End of Question 33

Star A Star B

Apparent magnitude 0.34 13.16

Spectral class F5 A4

Luminosity (relative to Sun) 7.3 0.0063

Average separation 2.2 × 109 km

O10–4

10–2

1

102

104

+15

+10

+5

0

–5

–10

B ASpectral type

Herzsprung-Russell Diagram

Lum

inos

ity (

sola

r un

its) A

bsolute magnitude

F G K M

1.0

0 10 30 50Time (years)

Light Curve for the Binary System

Rel

ativ

e br

ight

ness

70

6

End of Question 33

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Question 34 — From Quanta to Quarks (25 marks)


(a) (i) Using diagrams and text, outline Bohr’s explanation of the Balmerseries.

(ii) Outline TWO observations from atomic emission spectra that could notbe fully explained by the Rutherford-Bohr model.

(b) (i) What are the requirements for an uncontrolled nuclear chain reaction?

(ii) How does the equivalence between mass and energy relate to whatoccurs during the natural radioactivity process?

(c) How can neutrons be used to probe the positions of nuclei within the structure ofa metal crystal? Make reference to the work of Louis de Broglie in your answer.


(d) (i) Explain how the internal structures of the proton and neutron determinetheir properties.

(ii) How are accelerators used to investigate the structure of matter?

(e) Describe the role of conservation laws in the development of atomic physics.

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End of paper

© Board of Studies NSW 2012

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460 Exce l S U C C E S S O N E H S C • P H Y S I C S


2012 HSC Examination PaperSample Answers

Section I, Part A (Total 20 marks)

1 D The coil is being rotated in a magnetic field; therefore, it will generate a voltage (a generator). The generator has a split-ring commutator, thus it will supply fluctuating DC to the meter.

2 A The speed of light is used today to define the metre, i.e. 1.00 m is the distance light

will travel through a vacuum in 1c seconds, where c is the speed of light (constant).

3 C The position of the cathode ray is observed as light is emitted when the electrons in the beam strike the fluorescent screen.

4 B Now DEp 5 Epf 2 Epi. From the graph, DEp 5 25.8 3 109 2 (23 3 109) 5 22.8 3 109 J.

5 C The Group 3 element used for a p-type semiconductor is gallium.

6 C Electric field strength is indicated by the density of lines, i.e. C indicates double the field strength.

7 B In order for taI, the magnetic field influencing the motor coil must remain uniform, i.e. a radial magnetic field is used.

8 A F 5 BIlsinu. Magnetic field is perpendicular to current, therefore 0.03 5 0.05 3 Il. From the diagram and considering trigonometry, l 5 0.4 m.

Therefore I 5 0.0310.05 3 0.4 2 5 1.5 A.

9 B Low Earth orbit satellites travel at a higher orbital velocity with a shorter period when compared to a geostationary satellite.

10 D In order to convert 20 V to 2 V, the number of loops in the transformer coils needs

to have a ratio of 10 to 1. V1

V25

n1

n2

11 C The gases being expelled down from the rocket engine create an equal and opposite reaction on the rocket engine, which acts upward.

12 A Fc 5 mv2

r and v 5

2prT

. Therefore, Fc 5 17.35 3 1022 3 4p2 3 3.83 3 102 212.36 3 106 2 2

5 2.0 3 1020 N towards Earth.

13 B Moon T

2

r 3 5 Satellite

T 2

r 3 , 12.36 3 106 2 211 2 3 5

T 210.5 2 3 , T 5 8.34 3 105 s


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461Exce l S U C C E S S O N E H S C • P H Y S I C S

2 0 1 2 H S C E X A M I N A T I O N P A P E R • A N S W E R S

14 D Induced emf is at its maximum when change of flux is greatest, i.e. where the gradient of line is steepest on the flux versus time graph. Direction of induced emf acts to create a current that produces a magnetic field to oppose the change in flux. Flux versus time begins with the maximum positive slope, therefore induced emf begins at a maximum negative value, i.e. answer D.

15 D A property of superconductors is that they exclude magnetic fields from entering them.

16 C With no load on the ideal motor there is no energy being used, therefore the back-emf being created will be about equal to the forward-applied voltage.

17 B FDl

5 kI1I2

d. Now I1 5 I2, d 5 0.002 and l 5 1.0 m. Therefore, since F 5 2.5 3 1023

then I 5 5 A.

18 C Fg 5 GmEmm

d2 . Now dy 5 4.5 units and dx 5 3 units, Fx

Fy 5

20.259

5 2.25.

19 C Electric power raises the temperature of the pot. The pot base has a low resistance. P 5 RI2. The more rapid the change in flux, the greater the induced emf. This creates a larger current and more rapid heating of the saucepan. Therefore C.

20 A Max. energy output from human 5 E

5 hf

5 hcl

5 6.626 3 10234 3 3 3 108

9 3 106

5 0.138 eV.

Therefore the band gap should be less than 0.138 eV. This makes HgCdTe the best choice.


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Section I, Part B

Question 21

(a) A simple pendulum was used where the length of the pendulum could be set to different values from 0.5 to 1.3 m. With the length set to 0.5 m, the time taken for the pendulum to complete 10 full oscillations was recorded. This was then repeated twice more.

The length of the pendulum was then adjusted, in turn, to each of 0.7, 0.9, 1.1 and 1.3 m and the time for 10 oscillations of each pendulum was recorded three times. From the data collected, the average period for each length was determined and a graph of length versus period squared was drawn.

Considering the slope of the graph is l

T 2 , and knowing from theory that g 5

4p2lT

2 ,

a value for g was determined by multiplying the slope of the graph by 4p2. (3 marks)

(b) The accuracy of the answer obtained from the experiment would be assessed by comparing the experimental answer with the actual value of g for our location using a reliable source (reference), e.g. the internet site for Geoscience Australia. (1 mark)

(c) The reliability of the answer could be increased by repeating the experiment several more times. (1 mark)

(d) The reliability could be assessed by seeing whether the answers obtained from the repeated experiment are the same or within 2% and whether the other groups performing the same experiment got the same answer. (1 mark)

Question 22

(a) As the coil is raised, the loops of copper wire cut magnetic fl ux and experience a changing magnetic fi eld. According to Faraday’s law, a voltage is induced when a conductor cuts magnetic fi eld lines and, as the circuit is complete, while the solenoid moves relative to the magnet the induced voltage will cause a current to fl ow in the solenoid loops. (2 marks)

(b) According to Lenz’s law, when a conductor experiences a change in magnetic fi eld the direction of the induced voltage will result in a current fl owing to create a magnetic fi eld in a direction to oppose the motion which created it. This means the bottom of the solenoid becomes a South magnetic pole as the solenoid moves and the induced current fl ows. This South pole attracts the North pole of the bar magnet in an equal and opposite reaction which initially acts up on the bar magnet. This upwards force results in a reduction in the reading on the electronic balance. As the solenoid moves further away, this force reduces and the reading on the balance will eventually return to its original value. (4 marks)


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Question 23

Being over the pole when released, mass A has no horizontal velocity and will accelerate vertically down due to the gravitational attraction of Earth. As it falls, the acceleration will

increase as it gets closer and closer to Earth, i.e. g a 1d

2 . The very high velocity achieved by

the time it nears Earth is likely to cause mass A to burn up as it begins to enter the increasingly dense atmosphere of Earth.

Mass B, when released at this distance from Earth, will remain exactly where it is. This is due to it being directly above the equator and having the same angular velocity as the surface of

Earth, i.e. it will be in a geostationary orbit with an orbital velocity, VB 5 ÄGmE

d, where d is

the distance from mass B to the centre of Earth. This velocity is just the right magnitude for mass B to remain in orbit at this distance directly above the equator. (4 marks)

Question 24

(a)

Conductionband

Conductionband

Conductionband

Forbidden zone(energy gap)

Forbidden zone(energy gap)

Valenceband Valence

band Valenceband

Conductor Semiconductor Insulator

(2 marks)

(b) The applied electric fi eld can provide the required energy for valence electrons to cross the forbidden zone and move to the conduction band, leaving a positive hole in the valence band. The electric fi eld causes movement of the electrons through the semiconductor against the fi eld (towards the positive side) while a hole current will fl ow with the fi eld towards the negative side. (3 marks)

Question 25

(a) When compared to transistors, thermionic devices consumed much more energy and produced more heat. They were also much larger and extremely fragile. The development of the transistor provided a more robust, much more effi cient and reliable device that could perform the same job more cheaply than thermionic devices. (2 marks)


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(b) The transistor has had an enormous impact on society, with its development and subsequent miniaturisation having led to its application in so many of our modern devices, e.g. microprocessors, computers and communications technology. The development of the transistor has led to the internet and the ability for humans all over earth to rapidly communicate and for news and images to be almost instantly spread worldwide. The transistor has allowed the development of cheap portable devices like mobile phones and this has dramatically changed our ability to communicate and receive information. (5 marks)

Question 26

According to the information, Design A lost 20 MW of power as the current travelled the 100 km distance in the transmission wires to the substation as only 100 MW arrived. The power lost from Design B can be calculated based on the loss in potential difference, 508 kV down to 500 kV at the substation, with the current travelling through the transmission lines

of 40 V resistance, i.e. power lost 5 V

2

R2

80002

40 5 1.6 MW. The superconductors in

Design C have no resistance to the transmission current but to cool the superconducting transmission lines requires power to be consumed, i.e. 30 kW per km over a distance of 100 km requiring a total of 3000 kW, i.e. 3.0 MW.

Based on the results, the most efficient system is Design B using the higher voltage, i.e. 500 kV. At this voltage, only 1.6 MW was consumed to transmit the 100 MW of power to the substation compared with 3.0 MW for the superconductor lines of Design C and 20 MW for the lower voltage (33 kV) of Design A. (6 marks)

Question 27

Vertical displacement, sv 5 34 m up, horizontal displacement, sy 5 45 m right.

For vertical motion, sv 5 uvt 1 12

avt2, i.e. 34 5 2usin60°t 1 4.9t2. Equation 1

For horizontal motion, sh 5 uht, i.e. 45 5 ucos60°t, 450.5

5 ut. Equation 2

Combining the two equations, 234 5 20.866 3 90 1 4.9t2.

Therefore, t 5 Å77.94 2 344.9

5 2.99s.

Substituting into Equation 2, u 5 45

2.99 3 0.5 5 30.1 ms–1

up at 60° to horizontal.

(4 marks)

uh

uv

60°

u


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Question 28

(a) The following are two examples of evidence for relativity.

Particle accelerators must be constructed to allow for the relativistic effects for the very high velocity particles being studied, i.e. increased masses and length contraction.

GPS atomic clocks must be corrected for time dilation (Special theory) because of their high speed and time changes due to the variation in the gravitational fi eld (General theory). (2 marks)

(b) The theory must be testable by experiment and make predictions which can be verifi ed by measurements. Suitable experiments must be designed which can explore whether the predictions of the theory are observed and supported by the results. The experiments will involve the use of accurate measuring devices which are sensitive enough for the required measurements. For the theory to be validated, the experiments must follow the scientifi c method with suitable controls and when repeated be found to always produce results that are consistent with the predictions of the theory. (3 marks)

(c) ly 5 l0 Å1 2v2

c2 . The electron considers the tube to be moving relative to it. Therefore

ly 5 0.4Å1 21014

1016 , ly 5 0.398 m. According to the electron, the distance is 39.8 cm.

(2 marks)

Question 29

An AC current flows into the coil of the loudspeaker, which is directly attached to the speaker cone. The outer edge of the speaker cone is mounted on rigid supports with the centre on flexible mountings. The AC flowing in the coil produces a magnetic field which interacts with the external magnetic field created by the surrounding permanent magnet. The alternating current results in a changing magnetic force acting on the coil causing it to move back and forth due to the motor effect. As the coil is attached to the speaker cone and is free to move, it oscillates back and forth causing the membrane of the speaker cone to vibrate at a frequency equal to the frequency of the AC passing into the coil. As a result the vibrating speaker cone produces a sound of a frequency equal to the frequency of the AC passing into the coil with the volume of the sound related to the size of the electric current flowing in the coil, i.e. the force acting on the coil moving the speaker cone is directly proportional to the AC flowing in the coil. The AC supplied to the coil varies in frequency and form to produce the different frequency sounds and voice from the speaker.


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AC electric current flowing to coil

Speaker cone

Coil of copper wire

Permanent magnet (poles indicated)

N

S

N

(5 marks)

Question 30

(a) The particles have opposite electric charges, with P positively charged and Q negatively charged. (1 mark)

(b) The paths are circular because the magnetic force acts perpendicular to the initial velocity of the particles and as such it is a centripetal force which produces a circular path. The fact that the circular paths are uniform shows that the particles are experiencing a constant centripetal force with no resistance to their motion (travelling in a vacuum) and they are moving at a constant speed. (2 marks)

(c) The magnetic force acting on the charged particle is given by F 5 Bqv. This creates

a centripetal force i.e. Fc 5 mv2

r. Therefore, Bqv 5

mv2

r. Rearranging gives r 5

mvBq

.

As can be seen from the equation, the radius of the curving path is proportional to the mass and velocity of the particles, and inversely proportional to the charge of the particles and the strength of the external magnetic fi eld. (2 marks)


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Section II—Options

Question 32—Medical Physics

(a) (i) X-rays are made by exposing photographic fi lm with X-rays produced using cathode ray tubes. Both photographic fi lm and cathode ray tubes were available in 1895.

However, computerised axial tomography not only requires the use of a cathode ray tube to produce X-rays, it also requires the use of electronic X-ray detectors and sophisticated computer technology which was not available until 1972. Hence, CAT scan imaging could not be developed until the required computer technology was developed. (2 marks)

(ii) PET (positron emission tomography) provides functional information as ‘fuzzy’ images about specifi c target organs/structures within the body but cannot provide detailed anatomical images, whereas CAT (computerised axial tomography) provides detailed structural information about organs and structures of the body in the form of high quality images of thin slices but cannot provide detailed functional data.

For example, a PET scan of the brain can be used to detect regions of the brain that are underactive whereas a CAT scan clearly shows the structure of the brain without detecting the abnormality. For this reason CAT and PET are often used in conjunction so that areas of abnormality can be more specifi cally located. (2 marks)

(iii) PET is based on the detection of gamma radiation emitted from places within the body where a specifi c radiopharmaceutical, which has been introduced to the body via inhalation or injection, has been absorbed. The gamma rays are emitted as a result of the positron decay of specifi cally chosen positron-emitting radioisotopes. The positrons emitted from the radioactive nuclei (e.g. carbon 11, oxygen 15, fl uorine 18) annihilate with electrons in the body. Each annihilation event produces two gamma rays which travel in opposite directions. It is these gamma rays that are detected and used to make the image. The radioisotopes are typically produced in a cyclotron.

CAT relies on the production of X-ray radiation which is directed through the body. The X-rays are produced in a cathode ray tube. Electrons from a heated cathode are accelerated by a strong electric fi eld, to high velocity, towards an anode. When the electrons strike the anode, they undergo rapid deceleration and loss of kinetic energy. This deceleration of the electrons causes the production of useful X-rays called Bremsstrahlung radiation. The desired range of frequencies of X-rays used is determined by adjusting the potential difference between the anode and the cathode and through the use of fi lters. (3 marks)


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(b) (i) Inside a person there are countless billions of hydrogen atoms. The nuclei of these hydrogen atoms ‘spin’ and the axes of spin ‘wobbles’ like a spinning top. This wobble is called precession. Prior to the radio pulses being administered into the patient, a strong magnetic fi eld is applied and the hydrogen nuclei are affected by the fi eld, such that the axes of their precession are either parallel or anti-parallel to the fi eld. The frequency of their precession under these conditions has a defi ned value which is proportional to the strength of the magnetic fi eld, called the Larmor frequency. A gradient magnetic fi eld is also applied which provides small, but signifi cant, variations in the strength of the magnetic fi eld and hence resonance frequencies of the hydrogen nuclei, across the patient’s body. The radio pulses have a range of frequencies which match the frequencies of the precessing hydrogen nuclei. Hydrogen nuclei absorb energy from the radio pulse that matches (resonates with) the frequency of their precession. When the energy is absorbed, the amplitude of the precession increases. This heightened energy state, however, is unstable and the nuclei emit radio energy at the same frequency as the radio energy absorbed from the pulse, causing them to ‘relax’ back to the lower energy state. It is the emitted radio wave energy that is detected, measured and used to produce the magnetic resonance images. (3 marks)

(ii) Several advances in physics have contributed to the development of magnetic resonance imaging (MRI). These have included historical inventions such as RADAR which refi ned the production and reception of radio waves using special antennae and tuned circuits, and displaying the collected information as signals on a cathode ray screen.

Advances in computer technology included the development of the microchip which made it possible to process the large amounts of T1 and T2 data collected from the radio receivers. Software needed to be developed to allow, for example, the production of 3-D images that could be rotated to view in any direction and for the viewing of only particular tissue signals so that images, of perhaps just the blood vessels in the brain, could be made. The development of understanding about the importance of the gradient fi eld in the MRI machine made possible the voxel by voxel scanning required for 3-D imaging.

Developments in magnetic technology, such as the discovery and use of high-temperature superconductors in the electromagnetic coils of MRI machines, has enhanced the capabilities of MRI because it readily allows for the production of stronger, stable magnetic fi elds of the order of 1.5 to 3 Teslas and higher. The signals from the precessing protons are greater at higher magnetic fi elds because the ratio of parallel to anti-parallel alignment of the magnetic moments of the hydrogen nuclei is greater at higher fi eld intensities. This allows for stronger signals from the body tissues and thus greater resolution in imaging. (3 marks)


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(c) In order to be useful in medical imaging, a radioisotope should be readily accessible, produce penetrating radiation that can easily be detected, have a short half-life and cause little to no harm to the body. Tc99m has all of these properties.

• Water solubility. This is a useful feature because as a component of soluble salts, Tc99m is readily extracted from it using ‘COW’-containing insoluble salts of radioactive molybdenum (Mo99). The water solubility also makes the radiopharmaceutical produced from the Tc99m easy to administer into the body via the blood.

• Radioactivity. Tc99m emits gamma rays when it decays to Tc99. These gamma rays are useful because they are highly penetrating, can be detected using a gamma camera and are used to create an image.

• Short nuclear and biological half-life. The nuclear half-life of Tc99m is about 6 hours. In addition, because Tc99 is water soluble it is readily excreted via the kidneys in the urine. Thus it also has a short biological half-life. Together, these properties are useful because after a short period of time the person is effectively no longer radioactive. This reduces the likelihood of tissue damage to them and reduces the time they need to be isolated from other people. (3 marks)

(d) Endoscopes have a long thin tube that is surgically inserted into the body of a patient via a small hole. Inside the tube, there are two types of bundles of optical fi bres which are used when obtaining images of internal organs. Incoherent bundles of optical fi bres deliver light using the principle of total internal refl ection, into the body, to provide illumination of the organs to be viewed. The fi bres in these bundles are not specifi cally ordered (see the diagram) because they are only delivering the light. On the other hand, the optical fi bres used to ‘collect’ various pieces of the image must be in the same order at both ends (see the diagram). This is because each tiny fi bre refl ects light from only a small view of the organ being imaged by the camera (or eyepiece) at the outside end. In this sense, each piece of the image is like a pixel. For a clear image to be formed, the fi bres (hence pixels) must be in the same precise location at the camera end as they are at the organ end. The light refl ected from the internal organs travels along each fi bre in the coherent bundle via total internal refl ection. This total internal refl ection is achieved in all of the optical fi bres, in both types of bundles, because the fi bres are constructed from at least two layers of very clear glass with different refractive indices. The central core of the fi bres has a higher refractive index than the glass surrounding it. Since the fi bres are extremely thin, the angle of incidence of light travelling through the fi bres is so large that it is always greater than the critical angle for the surface between the two different layers of glass. Hence, the light is totally internally refl ected from the boundary between the layers and can travel from one end of the fi bres to the other with minimal loss of intensity.

1 1

2 2

3 3Coherent Incoherent

1 2

2 3

3 1

(3 marks)


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(e) There are three main types of ultrasound imaging techniques.

A-scans (amplitude scans) are used to make accurate measurements of distances. This type of scan does not result in a picture. It produces a refl ection intensity image in which the peaks of refl ected ultrasound can be used to determine distances to specifi c boundaries, e.g. between the retina and the back of the eye. This is useful in determining if the retina is attached or detached.

B-scans (brightness scans) are where the ultrasound transducer head may have one piezoelectric crystal (or many) to make the ultrasound waves. If there is just one crystal in the transducer, the transducer is rocked over the surface of the skin to produce an image of the structures below. The quality of the image is determined by the skill of the sonographer in rocking the transducer. Multi-crystal transducers can be held stationary over the expected location of the organ to be examined. Artifi cially controlled rocking of an ultrasound beam is achieved by electronic phasing of the signal from each of the piezoelectric crystals. This method produces straight waves, which provide much clearer images of structures within the body. B-scans can be used to produce still ‘pictures’ and multiple images taken over time can be sequenced to produce ‘video images’ of structures within the body. These images allow the health of a range of organs/tissues to be determined from measurements of their size and identifi cation of abnormal shapes, e.g. the growth rate of a foetus from the size of its head. Muscle tears and infl ammation of tendons and other soft tissue abnormalities such as breast tumours and ovarian cysts can also be determined.

Improvements in resolution, through the use of higher frequencies and improved transducer technology, have allowed signifi cant improvement in the size of structures that can be identifi ed and hence the quality of ultrasound images (e.g. amazingly detailed 3-D ‘photos’ and 4-D ‘video’ of foetuses while still in the womb). However, this use of higher frequencies has its limitations since, as frequency increases, attenuation increases, reducing the strength of the refl ections to be detected by the transducer. Resolution issues can therefore make the detection of very small abnormalities such as tiny breast tumours unlikely.

Doppler ultrasound scans can be used to ‘view’ and make real-time video images showing the movement of fl uids and surfaces inside the body. Examples include blood fl ow in arteries and inside the heart and movements of heart muscles and valves. In terms of diagnosis, this type of motion sensing can be used to detect heart health and issues such as leaking heart valves and constrictions in arteries. Colour enhancement of images is used to ‘see’ the direction and speed of blood fl ow in the images produced. It can also be used to add audio to video fi les, e.g. to hear the heartbeat of a foetus. Diffi culties in positioning the ultrasound probe to get the best angle on the movement being probed can limit the use of this technique.


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Ultrasound is, however, of little to no use in imaging the lungs, stomach and intestines due to the presence of air. The large difference in acoustic impedance between the air and the surrounding tissue effectively prevents the ultrasound from entering these areas and hence information about then is extremely limited. This air surface interface issue is also the reason for the need to apply acoustic coupling gel between the transducer and the skin; otherwise very little ultrasound would enter the body. Ultrasound is also of little use for imaging structures behind bone such as the brain and the regions inside joints. For example, almost no ultrasound penetrates through the skull and so ultrasound is not effective for imaging the brain. Very low refl ection percentages at tissue boundaries that have the same or very similar acoustic impedance do not allow for clear distinction on the image and hence limit the diagnostic ability for such situations. (6 marks)


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Question 33—Astrophysics

(a) (i) Photometry is the process of determining the distance away from Earth of celestial objects by measuring the light received from them.

The distance modulus formula is M 5 m 5 log10

d

10, where M is the measurement of

the absolute magnitude of a star, m is the measurement of its apparent magnitude and d is its distance away from us (Earth). In order to determine d using this method, both M and m are required. (1 mark)

(ii) There are similarities between the methods used by astronomers to obtain spectroscopic and photometric data, and also differences. In each procedure the objective of a telescope catches photons from the star, focuses them to a narrow beam and sends them to a charge-coupled device (CCD) within a ‘black box’, which counts them accurately. The reading is then converted by the computer into a measurement of m, the apparent magnitude of the celestial object being observed.

In the case of spectroscopic data, all the incoming photons entering the black box pass through one of two coloured fi lters. In this course, the fi lters are yellow-green (visual fi lter) and blue (photographic fi lter). The fi lters are regularly alternated. The apparent magnitude of the star as viewed through these fi lters will almost always be different. The colour index of the target star is defi ned using the formula: CI 5 B 2 V, which in this case becomes CI 5 mB 2 mV. (If, in fact, mB 5 mV it means that the star is white, an A0, as the colour index is an excellent way to determine the spectral class of the star.)

In the case of the photometric data, the light beam is passed through a diffraction grating to disperse the light into its spectrum. A thin collimator then moves across the spectrum very rapidly and repeatedly, allowing only a very narrow band of frequencies at any time to be passed to the CCD for counting. Each time the same band is measured increases the accuracy of the count, and when the observation interval is over the individual points of data are positioned on an apparent magnitude/wavelength graph called a spectrogram. In appearance this graph is an absorption spectrum, a blackbody curve superimposed by a large number of ‘valleys’ of distinct depths, allowing the star’s spectral class to be found. (4 marks)

(Teachers/students should note Syllabus 9.7.3, column 3, dot point 2, and 9.7.4, column 3 dot point 2. The CLEA exercises Spectral Classification and Photometric Photometry of the Pleiades are interesting, instructive ways for students to satisfy these requirements.)

(b) (i) The resolution of a telescope is defi ned as its ability to observe fi ne detail, i.e. to be able to separate two objects that are very close. Problems associated with ground-based optical astronomy that reduce their resolution include seeing and attenuation.


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Seeing is the apparent movement of target celestial objects due to atmospheric effects such as turbulence. Even our eyes can notice stars twinkling and changing colour, and this effect is greatly increased when they are observed through powerful telescopes. Since the image is continually changing, fi ne details are diffi cult to observe.

Attenuation refers to the selective scattering by the air of some frequencies of light more than others, distorting the colour of the object being observed. Molecules in the atmosphere scatter short wavelengths far more than longer ones, the reason the sky is blue. The lower towards the horizon a telescope is observing, the further light has to pass through the air, increasing this effect, which is why the sun appears red at dawn or dusk. (3 marks)

(ii) The resolution of ground-based telescopes can be improved in several ways, including adaptive optics (that corrects for the problem of seeing), and interferometry, where data received by separated individual objectives is combined by computers, yielding an image with the resolution of a single objective with a diameter equal to their distance apart.

(c) (i)

(2 marks)

(ii) When stars form within nebulae, they are initially composed of the material of the nebula, almost entirely hydrogen (80%) and helium (20%). Once fusion reactions have begun within the cores of stars, the hydrogen nuclei there join, forming helium and releasing a vast amount of energy. When the hydrogen within the core is exhausted, the star evolves. Many stars, including the Sun, become red giants, fusing helium to carbon in the central core, and more hydrogen into helium in a surrounding shell. Stars far more massive than the Sun evolve further, and fusion reactions permit the synthesis of many other elements, but only as far as iron.

Main sequencestar

Red giant

evolves

Mass?

Planetary nebula

White dwarf

evolves

< 1.4 Mo> 1.4 Mo

< ~8 Mo > ~8 Mo

Neutronstar/pulsar

Black hole

Mass?

Supernova


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The most signifi cant events known in the universe that allow so many other elements to be synthesised are supernovae. When the nuclear fuel of stars with very large masses is exhausted so the radiation pressure can no longer restrain the gravitational pressure crushing inwards, the star implodes. Atoms collapse into nuclei and the gigantic loss of gravitational potential energy is converted into heat resulting in a supernova, an explosion lasting for several weeks, during which fusion reactions do not need to be exothermic. In this situation the massive explosion not only synthesises all naturally occurring elements but a large number of highly unstable isotopes as well, blasting them off in all directions to become the metals scattered like fi ne dust in the nebulae where new stars may form eventually, with new planets as well.

Supernovae are thought to be the only way these elements can ever become available. (3 marks)

(d) (i) E

F

Position 1

Position 2 (6 months later)

Sun

1 A

U

Earth’s orbit S

Star

The distance to nearby stars is frequently measured by trigonometric parallax. The star is observed through a telescope with a very accurate direction marker, both ‘now’, when at position 1, and again six months later, when the Earth is on the opposite side of the Sun. This provides the largest base for observing the star currently available. The slight difference between the two measured readings is called the 6-month parallax angle of the star. One parsec is defi ned to be the distance away for which the average radius of Earth’s solar orbit subtends an angle of exactly 1 arcsecond. This, of course, provides a baseline of 1 AU (astronomical unit), so the measured 6-month parallax angle must be halved to determine the true 3-month parallax angle. The distance away of that star (in parsec) is

found using d 51

p". (3 marks)

(ii) Again, ground-based telescopes are at a disadvantage when using trigonometric parallax to measure the distances to stars because atmospheric effects limit their resolution. As a consequence, the furthest distance that can be determined using parallax is just 30 pc. (1 mark)


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(e) The binary consists of two stars, Star A, an F5 type, and Star B, an A4 type.

By comparing their apparent magnitudes using I1

I21 5 100

m2 2 m1

5,

we fi nd IA

IB1 5 100

13.16 2 0.345

.

This shows that Star A is 134 000 times brighter than Star B. Since both stars are the same distance from Earth, clearly star B must be a white dwarf, while Star A is a yellow-white main sequence star. This is confi rmed by the data for their luminosities relative to the Sun, and also using the H-R diagram. Their positions should be marked on the given H-R diagram.

Comparing the luminosities of Star A and the Sun, given to be 7.3 : 1, allows the absolute magnitude of Star A to be determined in the same way. Taking the absolute magnitude of the Sun to be 5, the absolute magnitude of Star A is shown to be 2.84. The H-R diagram confi rms this value for an F5 star. The distance formula used to determine the distance

of the binary is M 5 m 5 log10 d

106 2.84 5 0.34 5 log10

d

10, so d 5 3.16 pc.

The Light Curve shows that the period of the variable is 40 years. It also shows that the eclipse causes total occlusion, since the base of each trough is horizontal. The smaller dips correspond to when Star B is eclipsed; Star A is eclipsed when the larger dips are shown.

The combined mass of the two stars can also be approximated, given their average separation of 2.2 3 109 km 5 2.2 3 1012 m, while T 5 40 3 365 3 24 3 3600

5 1.262 3 109 s.

M1 1 M2 54p2a3

GT 2 5

4p2 12.2 3 1012 2 316.67 3 1011 2 11.262 3 109 2 2 5 3.96 3 1030 kg

Finally, approximating the orbits of the two stars about their common centre of mass,

their average orbital speed can be estimated: v 52paT

52p 12.2 3 1012 211.262 3 109 2

5 1.095 3 104 ms21. (6 marks)


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Question 34—From Quanta to Quarks

(a) (i) Bohr described the hydrogen electron as having allowable energy levels (stationary

states) with a quantised angular momentum given by the formula mvr 5 nh2p

, where

n is an integer 1, 2, 3 and so on, and h is Planck’s constant. When the electron moved from a higher energy level to a lower energy level, a photon of light was emitted with an energy corresponding to the difference between the two allowable energy levels, i.e. hf 5 Ei 2 Ef. Bohr’s model accurately predicted the Balmer series of spectral lines for hydrogen with the electron moving from a higher energy level down to the n 5 2 stationary state, as shown in the diagram.

n 5 6n 5 5n 5 4n 5 3

n 5 2

n 5 1

400 nm 700 nm

(3 marks)

(ii) Two observations from atomic emission spectra that could not be fully explained.

• The model only worked well for hydrogen and could not accurately describe the emission spectra of larger atoms.

• The model could not explain the relative intensity of the spectral lines observed, i.e. how bright each spectral line appeared. (2 marks)

(b) (i) For an uncontrolled nuclear chain reaction there must be a suffi cient concentration and arrangement of fi ssionable nuclei (a critical mass), e.g. U-235 or Pu-239, and neutrons must be produced in the fi ssion and go on to create fi ssion in another fi ssionable nucleus with the number of neutrons yielded increasing rapidly and causing further fi ssion reactions. (3 marks)

(ii) In order to provide the energy released in the radioactive decay, the mass of the parent radioactive nucleus must be greater than the combined mass of the nucleus of the daughter element forming and the emitted radiation (a, b or g). Since E 5 mc2, the energy for the decay comes from the loss of mass which occurs as the radioactive nucleus decays. The loss of mass is converted to kinetic energy carried by the radioactive emission and daughter nucleus formed. (3 marks)


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(c) The neutron has no charge and as such experiences no electrical interactions with electrons and the atomic nuclei of the sample being studied. This allows them to

penetrate deeply into a sample. According to the deBroglie equation, the wavelength of

a matter particle is given by the equation g 5 hp

, where h is Planck’s constant and p is

the momentum of the particle. In order to study the metal crystal a beam of neutrons, usually from a nuclear reactor or spallation, are passed through guides to produce a monochromatic beam (single wavelength). This beam is then directed at the target metal crystal. Since the neutron wavelength is very small, they can be used to locate the position of the atomic nuclei within the metal crystal. The neutrons are scattered in their interactions with nuclei and undergo diffraction and interference to allow the location and size of the nuclei to be determined. The information collected can also reveal the magnetic properties and movement of the nuclei. (4 marks)

(d) (i) Both particles are colour charge neutral and composed of three quarks which exchange gluons to combine via the strong interaction. The particles are very similar in mass with the neutron just a little more massive due to the down quark being more massive than an up quark. The up quark has an electric charge of

123

while the down quark is 213

. This results in an electric charge of 11 for the

proton and no net charge on the neutron. Both particles have an intrinsic angular

momentum (spin) of 12

.

u

ud

ud

d

neutronproton

(3 marks)

(ii) Accelerators are used to deliver energy to matter particles, e.g. electrons and protons. This raises the velocity of the particles until they are approaching the speed of light. As the speed of the particles begins to approach the speed of light, much of the energy being delivered by the accelerator goes to increasing the relativistic mass of the particles. These high-energy particles are then directed at a target or, as in the Large Hadron Collider (LHC), protons are collided with anti-protons travelling in the opposite direction. These high-energy collisions yield an array of subatomic particles with many of them having a larger mass than the rest mass of a proton. In this way the accelerators provide enough energy to the normal matter particles to allow the study of other particles that do not normally exist. These studies with accelerators have allowed the true building blocks of atoms, and the interactions between them, to be studied and allowed testing of the ideas of the present Standard Model. (2 marks)


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(e) The conservation laws have been fundamental to the development of atomic theory from the earliest times with many early scientists using conservation of mass to develop their model of atoms, e.g. John Dalton.

Einstein’s equation, E 5 mc2, explained where the energy for radioactive emissions came from as the decaying nucleus was heavier than the combined mass of the daughter nuclei and radioactive emission. This relationship between mass and energy became fundamental to the future studies of atoms.

Chadwick used conservation of momentum and energy in his famous experiment to confi rm the existence of the neutron which, at the time, was considered to complete our understanding of atomic structure.

The neutrino was originally proposed by Wolfgang Pauli in an attempt to explain the so-called missing energy in b-decay using conservation of momentum, energy and spin as the basis for his proposal.

The conservation laws continue to play an important role in predicting the behaviour and nature of matter and have provided a means to not only describe atoms but to also allow the development of a theory on how matter and the universe came to be as we fi nd it today. (6 marks)


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success one hsc physics

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