Photoelectric Effect

Quantum Physics Lesson 1

Comment made circa 1900 (Believed to be from Lord

Kelvin)

"There is nothing new to be discovered in physics now. All that remains is more and more precise measurement"

Learning Objectives

Describe the three main conclusions of the photo-electric effect.

Define the Electron Volt, Work Function & Threshold Frequency

State and use the photoelectric equation.

What is Light?

In the late 19th Century, scientists thought it was a wave and had lots of experimental evidence to back it up.

… but there was a problem…

Photoelectric EffectFirst observed in 1839, by Alexandre Edmond Becquerel.

If you shine light on to a metal it can emit electrons.

Safety

Don’t look directly into the laser! Put signs on the door.

UV only shines on zinc plate.

Photoelectric EffectTry this experiment and observe what happens when you shine a normal light, laser light and UV light on to the negatively charged metal plate.

Will the result be the same each time?

Make notes of your observations.

How can you explain your observations?

Photoelectric Effect

What if 100 What if 100 lasers were lasers were directed directed onto the onto the plate?plate?

Would that Would that have an have an effect?effect?

or

(Diagrams: resourcefulphysics.org)

Homework

Complete Past Paper Question – may need to look up answer to part (b)!

Complete worksheet but not questions that are crossed out – don’t need to know that bit!

I will post a link to some useful online notes over the weekend on Unit 1 page.

I will collect and mark next Thursday.

Significant Figures

1. All non-zero digits are significant. 2. In a number without a decimal

point, only zeros BETWEEN non-zero digits are significant. E.g. sig in 12001 but not in 12100

3. In a number with a decimal point, all zeros to the right of the right-most non-zero digit are significant. 12.100 5 s.f.

Use a Reasonable Number of S.F.

Try to use the same s.f. as those provided in the question or just one more.

Example: A man runs 110 metres in 13 seconds,

calculate its average speed. Speed = Distance/Time = 110 metres / 13

seconds =8.461538461538461538461538461538 m/s =8.46 m/s seems acceptable. If in doubt use 3 s.f. – can’t be too far wrong.

Recap

What is the photo-electric effect?

Three Main ConclusionsThree Main Conclusions1) For a given metal there is a minimum

frequency called the threshold frequency below which there is no emission.

2)2) Photoelectrons are emitted with a range of Photoelectrons are emitted with a range of KE from 0 up to a maximum which KE from 0 up to a maximum which increases as the frequency increases. increases as the frequency increases. Nothing to do with intensity.Nothing to do with intensity.

3)3) Number of photoelectrons emitted per Number of photoelectrons emitted per second is proportional to the intensity of second is proportional to the intensity of the incident radiation.the incident radiation.

AnalogiesAnalogies

If you’re stuck down a well you can’t get If you’re stuck down a well you can’t get out unless you have enough energy to jump out unless you have enough energy to jump out in one go – same for an electron.out in one go – same for an electron.

Coconut Shy – can fire 1,000 ping pong Coconut Shy – can fire 1,000 ping pong balls at a coconut – but they’re just ping balls at a coconut – but they’re just ping pong balls, not going to knock the coconut pong balls, not going to knock the coconut off!off!

It only takes one bullet though...that does It only takes one bullet though...that does have enough energy and momentumhave enough energy and momentum

What’s going on?What’s going on?

Why is this important?Why is this important?

Only conclusion 3 can be explained if Only conclusion 3 can be explained if light is a only a wave.light is a only a wave.

The other 2 conclusions can explained by The other 2 conclusions can explained by thinking of light as arriving in discrete thinking of light as arriving in discrete packets of energy called quanta.packets of energy called quanta.

Evidence that light consists of tiny Evidence that light consists of tiny particles called photons!particles called photons!

Definitions (From Past Papers)

The Work Function:- minimum energy to remove an electron

from the surface of a metal

The Threshold Frequency:- minimum frequency of electromagnetic

radiation required to eject photoelectrons from a metal surface

THE ‘ULTRAVIOLET CATASTROPHE’

1900 - RayleighThis was a CLASSICAL prediction, first made in the late 19th century, that an IDEAL BLACK BODY at thermal equilibrium will emit radiation with INFINITE POWER.

Max Planck resolved this issue by postulating that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in DISCRETE PACKETS OF ENERGY proportional to the frequency. He called these packets ‘QUANTA’.

hfE Note: sJxh .10626.6 34

Photon EnergyPhoton Energy We can work out the energy of an We can work out the energy of an

incoming photon:-incoming photon:- Symbol Equation:-Symbol Equation:-

Where E is the Energy of Photon in Joules (J)Where E is the Energy of Photon in Joules (J) f is the Frequency of the Radiation in Hertz (Hz)f is the Frequency of the Radiation in Hertz (Hz) h is Planck’s constant = 6.63 x 10h is Planck’s constant = 6.63 x 10-34-34 Js Js

Word Equation:-Word Equation:-Radiation ofFrequency ConstantsPlanck'EnergyPhoton

hfE

Photon EnergyPhoton Energy Recall from GCSE that f = c/Recall from GCSE that f = c/λλ so we so we

can substitute this into the photon can substitute this into the photon energy equation E=hf to get:energy equation E=hf to get:

Or in words:-Or in words:-

(m)RadiationofWavelength

)(msLight of Speed(Js)ConstantsPlanck'(J)EnergyPhoton

1

hc

E

Worked Example

Q: What is the photon energy for UV Q: What is the photon energy for UV radiation with a wavelength 400 nm?radiation with a wavelength 400 nm?

Worked Example Q: What is the photon energy for UV radiation Q: What is the photon energy for UV radiation

with a wavelength 400 nm?with a wavelength 400 nm? λλ = 400 nm = 400 x 10 = 400 nm = 400 x 10-9-9 m m E = ?E = ? h = 6.63 x 10h = 6.63 x 10-34-34 J s J s c = 3 x 10c = 3 x 1088 ms ms-1-1

J19-9-

-18-34

10 97.4m 10 400

ms 10 x 3 Js 10 6.63

hcE

The Electron VoltThe Electron Volt

Defined as:-Defined as:-

The amount of The amount of kinetic energy gained by a single unbound electron when it accelerates through an electrostatic potential difference of one volt.

Energy = Charge × Potential DifferenceEnergy = Charge × Potential Difference = 1.602×10= 1.602×10−19−19 C × 1 V = 1.602×10 C × 1 V = 1.602×10−19−19 J J

Note that 1 V = 1 JCNote that 1 V = 1 JC −1 −1

THE PHOTOELECTRIC EFFECT

1905 - Einstein

The emission of electrons from a surface (usually metallic) upon exposure to, and absorption of, electromagnetic radiation.

The photoelectric effect was explained mathematically by Einstein who extended the work on QUANTA as developed by Planck.

hKE

More EquationsMore Equations

The process of tearing an electron loose The process of tearing an electron loose takes up an amount of energy called the takes up an amount of energy called the work function,work function,ΦΦ, and the rest is , and the rest is converted into kinetic energy, Econverted into kinetic energy, EK(max)K(max)

So when emission occurs we use So when emission occurs we use Einstein’s equation:-Einstein’s equation:-

Or in Symbols:-(max)KEhf

Energy(J)KineticMaximum(J)FunctionWork(J)EnergyPhoton

More EquationsMore Equations When the light incident on the metal is at When the light incident on the metal is at

exactly the threshold frequency the exactly the threshold frequency the photons have just enough energy to free photons have just enough energy to free the electrons (i.e. the work function)the electrons (i.e. the work function)

In Symbols:-In Symbols:-

where fwhere f00 is the threshold frequency. is the threshold frequency.

0hf

(J)EnergyPhoton)(JFunctionWork

Learning Objectives

Describe the three main conclusions of the photo-electric effect.

Define the Electron Volt, Work Function & Threshold Frequency

State and use the photoelectric equation.

EinsteinEinstein

‘‘All the fifty years of conscious All the fifty years of conscious brooding have brought me no closer brooding have brought me no closer to the answer to the question, “What to the answer to the question, “What are light quanta?”. Of course, today are light quanta?”. Of course, today every rascal thinks he knows the every rascal thinks he knows the answer, but he is deluding himself.’ answer, but he is deluding himself.’

Physics WorkshopPhysics Workshop

Every Wednesday 3.40pm-4.40pm in O8Every Wednesday 3.40pm-4.40pm in O8

Is this time good for most people?Is this time good for most people?

Definition Capello verb1. To expect the very best.2. To not accept excuses.3. To get the job done.4. Get Lampard and Gerrard playing well in the same

team.

I’m going to Capello you! (well, apart from number 4)

Today’s ObjectivesToday’s Objectives

Explain the occurrence of line spectra Explain the occurrence of line spectra (e.g. of atomic hydrogen) as evidence of (e.g. of atomic hydrogen) as evidence of transitions between discrete energy levels transitions between discrete energy levels in atomsin atoms

Calculate the energy of emitted photons Calculate the energy of emitted photons using the equation hf = Eusing the equation hf = E11 - E - E22..

Explain what is meant by the terms Explain what is meant by the terms ionisation and excitationionisation and excitation

Enter and store numbers in your Enter and store numbers in your calculator.calculator.

Gas Discharge LampGas Discharge Lamp

When the gas-discharge lamp is switched on When the gas-discharge lamp is switched on the gas is ionised.the gas is ionised.

Free electrons, accelerated by the electrical Free electrons, accelerated by the electrical field in the tube, collide with gas and metal field in the tube, collide with gas and metal atoms.atoms.

Some electrons circling around the gas and Some electrons circling around the gas and metal atoms are excited by these collisions, metal atoms are excited by these collisions, bringing them to a higher energy state. bringing them to a higher energy state.

When the electron falls back to its original When the electron falls back to its original state, it emits a photon, resulting in visible state, it emits a photon, resulting in visible light or ultraviolet radiation.light or ultraviolet radiation.

QuantisationQuantisation A quantum mechanical system or particle that is A quantum mechanical system or particle that is

bound, confined spatially, can only take on bound, confined spatially, can only take on certain discrete values of energy, as opposed to certain discrete values of energy, as opposed to classical particles, which can have any energy.classical particles, which can have any energy.

These values are called These values are called energy levelsenergy levels. . The term is most commonly used for the energy The term is most commonly used for the energy

levels of electrons in atoms or molecules, which levels of electrons in atoms or molecules, which are bound by the electric field of the nucleus.are bound by the electric field of the nucleus.

The energy spectrum of a system with energy The energy spectrum of a system with energy levels is said to be quantized.levels is said to be quantized.

Emission SpectraEmission Spectra

Each element has its own specific set of lines.

SpectraSpectra

Emission spectraEmission spectra An energy input raises the electrons to An energy input raises the electrons to

higher energy levels. This energy input can higher energy levels. This energy input can be by either electrical, heat, radiation or be by either electrical, heat, radiation or particle collision.particle collision.

When the electrons fall back to a lower When the electrons fall back to a lower level there is an energy output. This occurs level there is an energy output. This occurs by the emission of a quantum of radiation.by the emission of a quantum of radiation.

When ever possible, electrons occupy the When ever possible, electrons occupy the lowest energy level called the lowest energy level called the ground ground statestate..

Electron in orbit round a nucleus in an atom

Energy input. The electron is excited and rises to a higher energy level (shell).

The electron falls back to its original energy level and energy is emitted in the form of radiation. The bigger the drop the greater the energy emitted and the shorter wavelength the radiation has (blue light).

Equation

In words:-

In Symbols:-

levelsenergybetweendifferencephotonemittedofEnergy

21 EEhf Note that E1 and E2 refer to the energies of the energy levels and hf is the energy of the photon emitted when an electron falls from the higher level to the lower level.

Energy LevelsEnergy Levels

“Why do the states have negative energy?” •This is because the zero of energy is considered to be that of a free electron 'just outside' the atom. •All energy states 'below' this – i.e. within the atom are therefore negative. •Energy must be put into the atom to raise the electron to the 'surface' of the atom and allow it to escape.

The Electron Volt (Again)

An electron volt is the kinetic energy gained by an electron when it is accelerated through a potential difference of 1V.

W=QV W=1.60 x 10-19 C x 1 V (V=JC-1) W=1.60 x 10-19 J = 1eV

Let’s try convert an energy (eV J)

Definitions Ionisation When an atom loses an orbiting electron When an atom loses an orbiting electron

(and becomes charged) (and becomes charged) from exam. from exam. An electron is removed from an atom

(making it a positive ion). from exam. from exam.

Comment: Would gaining an electron also count as ionisation?

Excitation An electron is raised to a higher energy

level but remains within the atom.

Definitions

Ground state – the lowest energy level of an atom.

Excited State – when one or more of an atom’s electrons moves to an outer shell at higher energy. An energy input raises energy input raises the electrons to higher energy levels.the electrons to higher energy levels.

Absorption spectraAbsorption spectra When light of all frequencies is passed When light of all frequencies is passed

through a gas then the gas absorbs through a gas then the gas absorbs light of the same frequency as it would light of the same frequency as it would emit.emit.

The light is radiated in all directions The light is radiated in all directions causing a reduction of intensity in the causing a reduction of intensity in the direction of the observer (dark lines).direction of the observer (dark lines).

And so is seen when emitted energy is And so is seen when emitted energy is absorbed by a medium. absorbed by a medium.

How do we get emission How do we get emission spectra?spectra?

Quick Question

Evaluate:-

using your calculator.

?35

30

Physics WorkshopPhysics Workshop

Every Wednesday 3.40pm-4.40pm in O8Every Wednesday 3.40pm-4.40pm in O8

Is this time good for most people?Is this time good for most people?

Homework For Friday 18th September:-

Research using books & the internet

How do fluorescent tubes work? Why are they used? Use the words ionisation and excitation in

your answer.

Don’t copy and paste put in your own words!

Today’s ObjectivesToday’s Objectives

Understanding of ionisation and Understanding of ionisation and excitation in the fluorescent tube excitation in the fluorescent tube Homework.Homework.

Calculator (Calculator (Order of Operations, Order of Operations, BODMAS).BODMAS).

Re-arrange equations.Re-arrange equations. Use prefixes & Converting between Use prefixes & Converting between

unit magnitudes.unit magnitudes.

Extra point to note

One photon releases one photo-electron.

Order of Operations B - Brackets first O - Orders (ie Powers and Square Roots, etc.) DM - Division and Multiplication (left-to-right) AS - Addition and Subtraction (left-to-right)

30 ÷ 5 × 3 =6 × 3= 18 Left to Right is the conventional order and is what your calculator does.

30 ÷ 5 × 3 =30 ÷ 15= 2 For this to be the case brackets would have to go around the (5 × 3)

Note that the fact that the 5 and 3 are put on the bottom on the previous slide implies they should be multiplied first. ?

35

30

Rearranging Practice

a = bc a = b/c a = b – c a = b + c a = bc + d a = b/c – d a = bc/d a = (b + c)/d a = b/c + d/e

b=?b=?, c=?c=?b=?c=?c=?d=?. b=?c=?e=?

Rewrite Without the Prefix

4 kW = 10 μC = 24 cm = 340

MW = 46 pF = 0.03 mA = 52 Gbytes = 43 kΩ = 0.03 MN =

Calculator Practice (7.5 x 103) x (24) = (6.2 x 10-5) x (5.0 x 10-3) = (1.4 x 105) x (2.0 x 104) = 4.5 x 103 / 7.0 x 104 = 4.3 x 10-6 / 6.0 x 103 =

Exercise B In each case, find the value of “y”. y = (7.5 x 103)2 2. y = (1.3 x 103) x (1.6 x 10-4) (6.6 x 106) + (3.27 x 10-3) 3. y = (5.6 x 10-4)2 x (7.8 x 108) (6.6 x 10-11) x (9.1 x 10-2)2 4. y = (4.12 x 103) + (6.5 x 102) (2.3 x 104) x (8.1 x 102)

Converting between Unit Magnitudes

Convert the following: 5.46m to cm 65mm to m 3cm to m 0.98m to mm 34cm to mm 76mm to cm

How many seconds are there in an hour? How many m are there in a km? Convert 33km/hr into m/s: Hint: Can you go further in an hour or a second? What is 1 mm3 in m3? Hint: try drawing a 1mm3 and converting its sides first What is 24cm3 in m3?

Wave-Particle DualityWave-Particle Duality

Quantum PhysicsQuantum Physics

Today’s ObjectivesToday’s Objectives

Explain what is meant by wave-particle Explain what is meant by wave-particle duality.duality.

Describe the main points of de Broglie’s Describe the main points of de Broglie’s hypothesis that matter particles also have a hypothesis that matter particles also have a wave-like nature.wave-like nature.

State and use the equation State and use the equation λλ = h/p = h/mv = h/p = h/mv

Describe evidence for de Broglie’s hypothesis.Describe evidence for de Broglie’s hypothesis.

Wave particle dualityWave particle duality

We have seen……………..We have seen……………..

Photons : Quanta (particles) of light

Electrons: Being diffracted. A property of waves

Prince Louis de BrogliePrince Louis de Broglie1892-19871892-1987

Electrons should not Electrons should not be considered simply be considered simply as particles, but that as particles, but that frequency must be frequency must be assigned to them also.assigned to them also.

(1929, Nobel Prize (1929, Nobel Prize Speech)Speech)

De Broglie (1924)De Broglie (1924) Suggested that particles such as electrons Suggested that particles such as electrons

might show wave properties.might show wave properties. He summised that the He summised that the de Broglie de Broglie

wavelengthwavelength, , λλ was given by: was given by:

m = mass

v = velocity of the particle

mv

h

p

h

Note that:-• This is a matter wave equation not electromagnetic wave• The de Broglie wavelength can be altered by changing the velocity of the particle.

In words...In words...

momentum

constant sPlanck'h wavelengtBroglie de

velocitymass

constant sPlanck'h wavelengtBroglie de

The diffraction tubeThe diffraction tube

Summary of ExperimentSummary of Experiment

Beam of electrons directed at a thin Beam of electrons directed at a thin metal foil.metal foil.

Rows of atoms cause the electron Rows of atoms cause the electron beam to be diffracted in certain beam to be diffracted in certain directions only.directions only.

We observe rings due to electrons We observe rings due to electrons being diffracted by the same amount being diffracted by the same amount from grains of different orientations, at from grains of different orientations, at the same angle to the incident beam.the same angle to the incident beam.

What we should seeWhat we should see

Electron diffractionElectron diffraction 1927: Davisson & Gerner confirmed 1927: Davisson & Gerner confirmed

this prediction with experiments this prediction with experiments using electron beams.using electron beams.

They actually used a nickel target They actually used a nickel target instead of a carbon one (we used)instead of a carbon one (we used)

The wavelength they measured The wavelength they measured agreed with de Broglieagreed with de Broglie

There is a relationship between the There is a relationship between the accelerating voltage V and the k.e. of accelerating voltage V and the k.e. of the particlesthe particles

Diffraction effects have been shown forDiffraction effects have been shown for

Hydrogen atomsHydrogen atomsHelium atomsHelium atoms

Neutrons Neutrons

Neutron diffraction is an excellent way Neutron diffraction is an excellent way of studying crystal structures.of studying crystal structures.

DE BROGLIE WAVELENGTH

Prince Louis de Broglie - 1932

De Broglie discovered that all particles with momentum have an associated wavelength.

mv

h

p

h

What is the wavelength of a human being, assuming he/she weighs 70 kg, and is running at 25 m/s?

1.Find the wavelength of an electron of 1.Find the wavelength of an electron of mass 9.00 x 10mass 9.00 x 10-31-31 kg moving at 3.00 x kg moving at 3.00 x 101077 m s m s-1-1

2. Find the wavelength of a cricket ball 2. Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m sof mass 0.15 kg moving at 30 m s-1-1..

3. It is also desirable to be able to 3. It is also desirable to be able to calculate the wavelength associated calculate the wavelength associated with an electron when the accelerating with an electron when the accelerating voltage is known. There are 3 steps in voltage is known. There are 3 steps in the calculation. Calculate the the calculation. Calculate the wavelength of an electron accelerated wavelength of an electron accelerated through a potential difference of 10 kV.through a potential difference of 10 kV.

Step 1: Kinetic energy Step 1: Kinetic energy EEk = k = eVeV = 1.6 x 10 = 1.6 x 10-19-19 x 10000 = 1.6 x 10 x 10000 = 1.6 x 10-15-15 J J

Step 2: Step 2:

EEKK = ½ mv = ½ mv22 = ½m (mv) = ½m (mv) 22 = p = p22 / 2m, / 2m, so momentumso momentum

pp = √2 = √2mEmEkk = √2 x 9.1 x 10 = √2 x 9.1 x 10-31-31 x 1.6 x 10 x 1.6 x 10-15-15 = = 5.4 x 105.4 x 10-23-23 kg m s kg m s-1-1

Step 3: Wavelength Step 3: Wavelength l = l = hh / / pp = 6.63 x 10 = 6.63 x 10-34-34 / 5.4 x 10 / 5.4 x 10-23-23 = 1.2 x 10 = 1.2 x 10--

1111 m m = 0.012 nm.= 0.012 nm.

Slits

Laser

Screen 1

L1

Slit spacing, dWavelength, Distance to screen, LFringe spacing, x

Screen 2L2

d1d2

Constituents of the AtomConstituents of the Atom

Particle PhysicsParticle Physics

Homework (Fri 2nd Oct)

Ernest Rutherford

What important experiment did he direct in the early 20th Century?

What did Rutherford conclude from his analysis of the observations?

Draw a lithium atom

This is the layout of a lithium atom, with three protons, three electrons, and four neutrons. The protons and neutrons are, of course, found in the nucleus. They are called nucleons. The electrons are found in shells orbiting the nucleus.

Today’s ObjectivesToday’s Objectives

State the charge and mass in SI units and State the charge and mass in SI units and relative units for the proton, neutron and relative units for the proton, neutron and electron. electron.

Define specific charge and calculate its value Define specific charge and calculate its value for nuclei and ions. for nuclei and ions.

Interpret nuclide notation including the Interpret nuclide notation including the Proton number Proton number ZZ and the nucleon number and the nucleon number A. A.

Define what is meant by isotope.

Important FactsImportant Facts

It is important to understand: It is important to understand: The nucleus is very small compared to The nucleus is very small compared to

the atom, about 10 000 times smaller. the atom, about 10 000 times smaller. The diameter of an atom is in the order The diameter of an atom is in the order of 10of 10-10-10 m, whereas the diameter of the m, whereas the diameter of the nucleus in the order of 10nucleus in the order of 10-15-15 m. m.

The atom is a very dynamic entity. The The atom is a very dynamic entity. The diagram shows a stylised diagram shows a stylised representation; the reality is that there representation; the reality is that there is absolute bedlam at the atomic level.is absolute bedlam at the atomic level.

Inside the atom…Inside the atom…

PropertyProperty ElectronElectron ProtonProton NeutronNeutron

ChargeCharge -1-1ee +1+1ee 00

MassMass 9.11 × 109.11 × 10--

31 31 kgkg1.67 × 101.67 × 10--

2727 kg kg1.67 × 101.67 × 10--

2727 kg kg

Relative Relative MassMass

1/18361/1836 1.00001.0000 1.00041.0004

The electron and the proton have the same value of charge, but the signs are different. We also use a quantity for the charge called electronic charge unit, e. 1 e = 1.602 × 10-19 C.

The neutron has a very slightly higher mass than the proton.

Definition of an IsotopeDefinition of an Isotope

Isotopes are atoms with the same Isotopes are atoms with the same number of protons and different number of protons and different numbers of neutrons.numbers of neutrons.

Quick Quiz

1) How many protons neutrons and electrons are there in the lithium atom?

2) A carbon atom has 6 protons and 6 neutrons. Draw out the carbon atom in a similar way to the lithium atom in the diagram above.

3) What is the total charge of a carbon nucleus?(a) in electronic charge units(b) in coulombs4) What is the total charge of the electrons?(a) in electronic charge units(b) in coulombs

Different atoms are distinguished by their numbers of protons and neutrons. We write the symbols using the following notation:

A is called the nucleon number, or the mass number. It is the total number of nucleons. Z is the proton number or the atomic number, which is the number of protons. The number of protons determines the element. X is the chemical symbol

Isotope Notation

Isotope Notation We can determine the number of neutrons

simply by subtracting the proton number from the nucleon number. ( No. of neutrons = A – Z).

Isotopes have the same numbers of protons, but different numbers of neutrons.

Isotopes have the same physical and chemical properties.

If the proton number is altered, the element changes.

Some isotopes are radioactive, as the nuclei are unstable.

Specific Charge

The specific charge of a charged particle is defined as its charge divided by its mass.

Calculate the specific charge for:-1) A hydrogen nucleus (1H).2) The electron.3) Doubly ionised 24Mg (mass is 3.98 x

10-26 kg).

Reactions Chemical reactions involve the electrons of

the outer shells. Nuclei are not involved in any way, and remain totally unaltered even in the fiercest chemical reactions.

Isotopes have the same numbers of protons, but different numbers of neutrons.

Isotopes have the same physical and chemical properties.

If the proton number is altered, the element changes.

Some isotopes are radioactive, as the nuclei are unstable.

Try this out… Carbon 14 is an isotope of Carbon. How many protons? How many neutrons? How many electrons?

Write out Carbon-14 using the isotope notation.

Carbon 14 is an unstable isotope. It decays so that one of the neutrons turns into a proton.

Draw the new atom, what is it? Write it out using the isotope notation.

Don’t mix up your ‘n’ words!

Nucleus – the massive positively charge centre of an atom

Neutron – an uncharged particle found in the nuclei of most atoms

Nucleon – a proton or a neutron in the nucleus

Nuclide – different types of nucleus of the same element but with different numbers of nucleons.

Summary

Strong Force & Strong Force & RadioactivityRadioactivityParticle Physics 2Particle Physics 2

Homework Reminder!

Ernest Rutherford

What important experiment did he direct in the early 20th Century?

What did Rutherford conclude from his analysis of the observations?

Today’s ObjectivesToday’s Objectives

The strong nuclear force:The strong nuclear force: -its role in keeping the nucleus stable;-its role in keeping the nucleus stable; - short-range attraction to about 3 fm, - short-range attraction to about 3 fm,

very-short range repulsion below about very-short range repulsion below about 0.5 fm0.5 fm

If time:-If time:- Equations for alpha decay and beta - Equations for alpha decay and beta -

decay including the neutrino.decay including the neutrino.

Size of the nucleus...Size of the nucleus...

If the atom were the size of the If the atom were the size of the school canteen, the nucleus would school canteen, the nucleus would be the size of a pea dropped in the be the size of a pea dropped in the middle.middle.

Really small compared to the atom!!Really small compared to the atom!!

For fun?...(don’t worry about the equations)

221

04

1

r

QQF

221

r

mGmF

Repulsive force between two protons.

Gravitational Attraction.

Q1,Q2=eG is gravitational constant.m are proton massesR is distance between the two protons (10-

15m).

Force Comparison Coulomb force of repulsion

is about 200N

Gravitational Force of attraction is only about 1.9×10-34 N.

So Coulomb force of repulsion is much, much stronger!!

21512

219

)101)(1085.8(4

)106.1(

CF

215

22711

)101(

)1067.1(1067.6

GF

Why doesn’t it fly apart?Why doesn’t it fly apart?

The repulsive force between the two The repulsive force between the two charges is much larger than the charges is much larger than the gravitational force.gravitational force.

So why is it stuck together?So why is it stuck together?

We need another force – the We need another force – the STRONG force.STRONG force.

The Strong Force GraphThe Strong Force Graph

Important to NoteImportant to Note

It’s a weird force!It’s a weird force!

At very short ranges, below 0.5 At very short ranges, below 0.5 femtometresfemtometres (0.5 × 10 (0.5 × 10-15-15 m) the m) the strong nuclear force is strong nuclear force is repulsiverepulsive. .

It is It is attractiveattractive up to its maximum up to its maximum range of 3 fm (3 × 10range of 3 fm (3 × 10-15-15 m). m).

Strong ForceStrong Force

What would happen if the strong What would happen if the strong force wasn’t repulsive at short force wasn’t repulsive at short distances?distances?

(protons would get pushed together)(protons would get pushed together)

It is about 200 N between two It is about 200 N between two protons – strong enough to counter protons – strong enough to counter the repulsive Coulomb force.the repulsive Coulomb force.

RadioactivityRadioactivity

Particle Physics 3Particle Physics 3

Radioactive DecayRadioactive Decay

Some isotopes are stable but others Some isotopes are stable but others are not.are not.

Those which are not release Those which are not release radiation and change into a more radiation and change into a more stable isotope (normally a different stable isotope (normally a different element).element).

How much do you know? Complete the table (in pencil) that describes the

properties of the three common radiations:-

Radiation

Particle Range in air

Stopped By

AnswersRadiation Particle Range in

airStopped By

Alpha Helium nucleus (P)

Few mm (P)

Paper (P)

Beta High speed electron (P)

Few cm (P)

Aluminium sheet (P)

Gamma Energetic photon (P)

Infinite (P) Several cm lead (P)

Alpha radiationAlpha radiation

Mostly comes from heavy nuclides with Mostly comes from heavy nuclides with proton numbers greater than 82, but proton numbers greater than 82, but smaller nuclides with too few neutrons can smaller nuclides with too few neutrons can also be alpha emitters. also be alpha emitters.

The general decay equation is summarised The general decay equation is summarised below. below.

The term The term QQ stands for the stands for the energyenergy.. Can be written with He as Can be written with He as αα and without and without

the Q.the Q.

Notes on Notes on αα-decay-decay

The alpha particle is a helium The alpha particle is a helium nucleusnucleus (NOT atom). (NOT atom).

Energy is released in the decay. The Energy is released in the decay. The energy is energy is kinetickinetic, with the majority going , with the majority going to the alpha particle and a little going to to the alpha particle and a little going to the decayed nucleus.the decayed nucleus.

The velocity of the alpha particle is much The velocity of the alpha particle is much greater than that of the nucleus. greater than that of the nucleus.

Example DecayExample Decay

The The nucleon numbernucleon number goes down by goes down by 4, the 4, the proton numberproton number by 2. by 2.

A typical alpha decay is: A typical alpha decay is:

Is this equation balanced? Explain Is this equation balanced? Explain your answer your answer

Beta radiationBeta radiation

Neutron rich nuclei tend to decay by Neutron rich nuclei tend to decay by beta beta minus (b-) emissionminus (b-) emission. .

The beta particle is a The beta particle is a high-speed high-speed electronelectron ejected from the nucleus, NOT ejected from the nucleus, NOT the electron clouds. the electron clouds.

It is formed by the decay of neutrons, It is formed by the decay of neutrons, which are slightly more energetic than a which are slightly more energetic than a proton. proton.

Isolated protons are stable; isolated Isolated protons are stable; isolated neutrons last about 10 minutes. neutrons last about 10 minutes.

Equation for Beta decay.Equation for Beta decay.

The neutron, having emitted an electron, is The neutron, having emitted an electron, is converted to a proton, and this results in converted to a proton, and this results in the proton number of the nuclide going up the proton number of the nuclide going up by 1. A new element is formed. The by 1. A new element is formed. The general equation is: general equation is:

Note the electron can be written as Note the electron can be written as ββ, also , also without the Qwithout the Q

Example Beta DecayExample Beta Decay

NotesNotes The nucleon number remains the same ; The nucleon number remains the same ; The proton number goes up by 1. The proton number goes up by 1. The beta particle is created at the instant of The beta particle is created at the instant of

the decay. the decay. The antineutrino is very highly penetrating The antineutrino is very highly penetrating

and has a tiny mass. It is very hard to detect. and has a tiny mass. It is very hard to detect. A precise amount of energy is released, A precise amount of energy is released,

according to the nuclide. according to the nuclide. That energy is shared among the nucleus, the That energy is shared among the nucleus, the

electron and the antineutrino. electron and the antineutrino.

Question Question

What is the balanced nuclear equation for What is the balanced nuclear equation for the following decays? the following decays?

(a) emission of a beta- particle from oxygen (a) emission of a beta- particle from oxygen 19 19

(b) emission of an alpha particle from (b) emission of an alpha particle from polonium 212 polonium 212

(c) emission of a beta + particle from (c) emission of a beta + particle from cobalt 56 cobalt 56

Proton numbers O – 8, F – 9, Fe – 26, Co – Proton numbers O – 8, F – 9, Fe – 26, Co – 27, Pb – 82, Po – 84 27, Pb – 82, Po – 84

AnswersAnswers

(a) (a)

(b) (b)

(c) (c)

Summary Summary

A graph of neutron number against proton A graph of neutron number against proton number shows that there are more neutrons number shows that there are more neutrons in larger nuclei in larger nuclei

This is needed to ensure stability of the This is needed to ensure stability of the nuclei. nuclei.

Natural decay occurs with alpha decay Natural decay occurs with alpha decay

Or beta minus decay. Or beta minus decay.

Particles & AntiparticlesParticles & Antiparticles

Particle Physics 4Particle Physics 4

Today’s Objectives

Compare rest mass energies of particles and anti-particles

Describe the processes of pair production and annihilation.

Calculate energies involved in pair production and annihilation.

Particle Physics Particle physics is concerned with

fundamental particles, which means that the particles can't be broken down any further..

It used to be thought that protons, neutrons and electrons were the fundamental particles of matter.

However it has been found that nucleons (proton and neutron) are made up of smaller particles, so nucleons are now not fundamental.

Paul Dirac (1902-1984) Wrote an equation

obeyed by an electrons which had a kind mirror image solution

Predicted the existence of anti-particles in 1928.

Discovery of the Positron Cosmic ray experiment. Charged particles leave

an ion trail as they pass through a super-cooled gas.

Causes vapour to condense to leave vapour trails – like jet plane.

Magnetic field causes charged particles to bend.

The particle bent the wrong way in a magnetic field.

Antiparticles

Each particle has an antiparticle. However, antiparticles are not found in normal matter, but arise in:

high-energy collision experiments,

interactions with cosmic rays,

radioactive decay.

Positron Emission

011YX A

ZAZ

Also called β+ decay.

Remember is isn’t a ‘natural’ form of decay – only occurs in experiments.

Happens when there are too many protons.

Notes

an antiparticle has the same mass as its particle,

a particle and its antiparticle have equal but opposite charge

an unstable particle and its antiparticle have the same lifetime.

some neutral particles and their antiparticles are identical (e.g. photon)

other neutral particles and antiparticles are not identical.

Complete this table

Particle Mass compared with proton

Charge

Electron 1/1800 -1e

Positron

Proton

Antiproton

Neutron

Antineutron

Albert Einstein From Einstein’s special

theory of relativity:-

Equivalence of energy and mass:

Energy can turn into mass Mass can turn into energy

Have a go! Calculate the rest mass energy of a proton in eV.

2mcE

Annihilation If a particle meets

with its corresponding anti-particle they annihilate.

All the mass of the particle and anti-particle mass is converted into energy in the form of photons (γ-rays).

0min producedphoton each ofenergy Minimum Ehf

Pair Production

Pair Production

0min 2 neededphoton ofenergy Minimum Ehf

In pair production a photon creates a particle and a corresponding anti-particle (usually e+ and e-).

Only occurs if one photon has enough energy to produce the total rest mass of the two particles.

Where fmin is the minimum photon frequency required, E0 is the rest mass energy of the particles.

antimatter andmatter of amounts equalget you mass into converted isenergy When

Cloud Chamber Pictures Can you see where pair production &

annihilation happen?

Cloud Chamber Pictures

Example Questions What is the rest mass energy of an

electron? What is the minimum energy required for

pair production of an electron and a positron to take place?

What is the minimum frequency required for pair production of an electron and a positron to take place? … and the wavelength?

To which part of the electromagnetic spectrum does this correspond?

Application - PET Scanners

Positron Emission Tomography

Positron emitting isotope is given to patient – some reaches the brain.

Positrons only travel a few mm before annihilating with electron and photons produced are detected.

Albert Einstein Showed that the mass of

a particle increases as its speed increases with the energy supplied to the particle to its increase mass by E=mc2.

The mass of a particle when it is stationary its rest mass (m0) corresponds to rest energy m0c2

Exchange Particles & Exchange Particles & Feynman DiagramsFeynman Diagrams

Particle Physics 5Particle Physics 5

Today’s Objectives Describe how forces are caused by

particle exchange. State that for the electromagnetic force,

virtual photons are the exchange particles

Draw Feynman Diagrams for the following interactions: Neutron-neutrino interaction Proton-antineutrino interaction β− decay β+ decay Electron capture

Exchange Particles

What causes forces?

Newton’s 2nd Law states that force is equal to the rate of change of momentum.

Momentum is calculated by multiplying the mass and the velocity of a particle.

Richard Feynman (1918 – 1988) came up with the idea that the forces are transmitted by exchange particles.

Feynman Diagram

Is a pictorial representation of what is going on.

First devised by American particle physicist Richard Feynman (1918 – 1988).

The forces between electrically charged particles are thought to be transmitted by photons, which are emitted and absorbed by the particles.

Weak Nuclear Force

Which force is involved when a neutron changes to a proton or proton neutron?

Can’t be electromagnetic because neutrons have no charge.

Must be weaker than the strong force otherwise it would affect stable nuclei.

Therefore it is called the weak nuclear force.

Weak Nuclear Force II

Due to the exchange of particles called W bosons.

They are unlike photons in that they have:-

Non zero rest mass A very short range (less than 0.001

fm!) Are positively or negatively charged.

Four Fundamental Forces

Type of Interaction

Exchange Particle/ Gauge Boson

Particles Affected

Strong Gluon Hadrons only

Electromagnetic

Photon Charged particles only

Weak W+,W−,Z0 All types

Gravity Graviton? All types

Feynman diagrams They were developed by Richard Feynman

to decribe the interactions in quantum electrodynamics (QED).

The diagrams are used to describe a variety of particle interactions.

Virtual particles are represented by wavy or broken lines and have no arrows.

Graphical ways to represent exchange forces, time is upward but the lines don’t represent the paths the particles take.

Proton-antineutrino interaction

Neutron-neutrino interaction

β− decay

β+ decay

Electron Capture

Electron-Proton Collision

Electron Capture II