Upper 6th – Unit 5

Nuclear Physics

Ideas about Atoms Timeline• 400 BC – Democritus – idea of atomism• 1803 AD – Dalton – elements made of atoms of different weights,

combine to make compounds• 1827 – Brownian motion reported – supports kinetic theory and

atomic model• Diffusion, also observed around this time, provides further support.• 1896 – Becquerel discovers radioactivity• 1897 – J J Thomson discovers the electron.• 1898 – Rutherford identifies alpha and beta rays.• 1899 – Thomson determines e/m for electron, develops

“plum pudding” model of the atom• 1907 – Thomson identifies the Proton and Isotopes• 1909 – Geiger & Marsden find evidence for the nucleus• 1913 – Bohr proposes that electrons exist in discrete orbits around

the nucleus• 1932 – Chadwick discovers neutron

Rutherford’s Atomic Model

• The familiar model we have was devised by Rutherford in 1910, working from evidence collected by Geiger and Marsden.

Geiger & Marsden’s experiment

• particles of fixed energy were fired at a thin gold foil and their paths measured.

• Most passed straight through the foil or were only slightly deflected, but a few (~1 in 10,000) bounced back.

• Alpha scattering

• Rutherford scattering

• G-M experiment simulation

• Force on alpha particles

The Geiger-Marsden experiment

• Why is it important that all a particles have the same KE?

• Why do you think they used a thin foil? Why gold?

• Why did the container need to be evacuated?

Ernest Rutherford

• “It was quite the most incredible event that has ever happened to me. It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back and hit you”

Rutherford’s Interpretation• Rutherford couldn’t explain these results using

Thomson’s “Plum pudding model” of the atom.• He concluded that atoms are mostly empty space,

with all the + charge and almost all mass concentrated in a small nucleus.

Estimating the size of the nucleus

• Only a particles passing close to the nucleus experience a significant deflection

Estimating the size of the nucleus

• Geiger & Marsden found about 1 in 10,000 particles were deflected by more than 90°.

• The foil used was a few 1000s of atoms thick (say n=104)• So the chance of an particle being deflected by a single

atom must be 1 in 10,000n.– This must depend on the ratio of the area of the nucleus

compared to the area of the atom• If D=atomic diameter and d=nuclear diameter,

• So d≈1/10,000.

n

Dd

D

d

n 10000 ,

41

41

10000

12

2

Alpha particle (+2e)

Gold nucleus (+79e)

d

Estimating Size of the Nucleus(KE converted to PE)

Size of the nucleus

Relative scales of atom and solar system

(Or a ball in a football stadium)

Structure of the atom

• Nucleus of protons and neutrons (“nucleons”), surrounded by electrons

• Helium atom• Mostly empty

space!• Electrons “orbit”

~105 nuclear radii away from centre

Seeing atoms• A scanning tunnelling

electron microscope image of the surface of a gold sample, with individual atoms visible.– “Stripes” caused by

surface crystalline detail

• Atoms of silicon

Size of nucleus by electron diffraction

• Remember that electrons can behave like waves? – They can be diffracted by objects of a similar

scale to their wavelength, just like light

Size of nucleus by electron diffraction – more accurate

• de Broglie wavelength: =hc/E• Diffraction pattern is superimposed on the

normal scattering pattern• First diffraction minimum is at an angle , where

sin =0.61/R (R is radius of nucleus)

How nuclear radius depends on A

• Using electron diffraction with samples of different elements we can measure R and A for different nuclides.

• By plotting a suitable graph it is possible to show that

– r0 is a constant, 1.05 fm

• Given data for R & A, what graph might you plot to find the above relationship?– See p. 177

31

0ArR

Volume proportional to mass, so nuclear density is constant.

Constant nucleon spacing – suggests strong force is same for all nucleonsArV 3

03

4

Nuclear Radiation

– Helium nuclei (2 neutrons and 2 protons)

– electrons (from the nucleus) (or positrons)

– photons (energy)

Nuclear Radiation

Properties of nuclear radiation

Cloud chamber observations

• Ionising radiation triggers the formation of droplets in a supersaturated vapour

• particles– Straight, radiate from

source– Same length (energy)

• particles– Easily deflected (light)– Less distinct (less ionising)

• video

Inverse Square Law

• Intensity is energy per second passing through unit area.

• For a point source, the Intensity is inversely proportional to the square of the distance from the source

• If the source radiates energy nhf per second,

2

1

rI

24 r

nhfI

Isotopes

• Different isotopes of a given element have different numbers of neutrons.

• So they have the same atomic number (Z) but different mass numbers (A).

• The chemical properties of the different isotopes of an element are identical, but they will often have great differences in nuclear stability

Isotopes

• For stable isotopes of light elements, the number of neutrons will be almost equal to the number of protons

• A growing neutron excess is characteristic of stable heavy elements.

• The element tin (Sn) has the most stable isotopes with 10

Nuclear Notation

Practice

• How many protons and neutrons is the following?

C146

U23892K40

19He42

Alpha emission

• An alpha particle consists of 2 protons and 2 neutrons– Like a helium nucleus

• So when an atom undergoes decay it loses 2 protons and 2 neutrons

• e.g.,

42

42

22488

22890 RaTh

Mass numbers balance

Charge numbers balance

Beta– emission

• A - particle is an electron which comes from a neutron-rich nucleus– A neutron changes into a proton, and an

electron and an antineutrino are emitted

• So when an atom undergoes – decay it gains 1 proton and loses 1 neutron

• e.g.,

01

eCaK 01

4020

4019

Mass numbers balance

Charge numbers balance

Beta+ emission

• A + particle is a positron (anti-electron) which comes from a proton nucleus– A proton changes into a neutron, and a

positron and an neutrino are emitted

• So when an atom undergoes + decay it gains 1 neutron and loses 1 proton

• eg:

01

eBC 01

115

116

Mass numbers balance

Charge numbers balance

Electron capture

• Some proton-rich nuclei can capture an inner shell electron, causing a proton to change into a neutron, with a neutrino emitted.

• An outer shell electron drops down to fill the lower shell, emitting an x-ray photon as it does.

eAreK 4018

4019

Mass numbers balance

Charge numbers balance

radiation produced by “rearrangement” of nucleus

Unstable Stable

Energy released

Same components

• So no change to the nuclear composition

Now do some practice…

• Fill in the missing parts:

• So how do you know what kind of radioactive decay an unstable nucleus will undergo?

?

?

?

?

?

?

?

?

The N–Z graph

• Provides a survey of nuclear stability– For light nuclei (Z<20)

N=Z for stable isotopes– As Z increases, stable

nuclei have increasing proportion of neutrons providing strong force ‘glue’

– Away from the stability curve, unstable nuclei decay to move closer to the stability curve

What does what?

• emitters occur for Z>60 or so. – They have more neutrons than protons, but just not

enough to overcome Coulomb repulsion.

• - emitters are on the left of the stability belt.– Neutron-rich nuclei can redress the balance by

converting neutrons to protons

• + emitters are on the right of the stability belt.– proton-rich nuclei can redress the balance by

converting protons to neutrons

Changes on the N-Z graph

• As shown opposite…• Many radioactive isotopes

decay to produce further unstable isotopes.

• It is possible for whole series of decays to be undergone before a stable daughter isotope is reached.– Such a series can be

represented on the N-Z graph by a series of arrows (see p. 173)

N

Z

Natural radioactive series

• figures in red are half-lives. Figures in boxes are averages for multiple paths.

U238 Th232

So when do you get ?

• Similar to electrons, nucleons only exist in allowed energy levels.

• Following the emission of an of particle the daughter nucleus may be formed in an excited state.

• This will be short-lived and the nucleus will move to its ground state, releasing the energy as a gamma ray (like photons produced when electrons de-excite).

Technetium – a pure emitter

• For medical imaging applications we want an isotope which– Has a reasonably short half-life– Only emits rays

• Technetium is formed in an excited state from the beta decay of molybdenum.

• The excited state is long lived (“metastable”, T1/2~ 6 h), so Tc can be separated from Mo to give the tracer required.

• See p.174 for more details

Activity

• The activity, A, of a radioactive isotope is the number of nuclei that decay per second.– Unit – becquerel (Bq)– 1 Bq = 1 decay per second.

• Radioactive decay is random, all undecayed nuclei have an equal probability of decaying at any time.

• The activity is proportional to the mass of undecayed isotope present.

• This mass decreases with time, due to decays, so the activity decreases with time too.

Activity gradually decreases

• Over time the activity of a sample will decrease

Half-life• Half-life (T1/2) is the time taken for half the

radioactive atoms in a sample to decay– or the time for the activity to drop to a half

• Activity after n half-lives is 1/2n times the original

1/2 1/2 1/2 1/2 1/2

1/2

Varying half-lives

• Half-lives for different substances range from seconds to many millions of years

• The most abundant isotopes are the most stable

Activity and Power

• A radioactive source of activity A emitting radiation of energy E is releasing energy at a rate AE per second.

• Power transferred = AE

• If such a source is sealed into a container, the container will gain thermal energy.

• This can be converted to electrical power in a Radioisotope thermoelectric generator, as used on many spacecraft.

Radioisotope thermoelectric generator

• Typically use plutonium-238 dioxide pellets:– best enegy/mass ratio– mostly useful radiation– longish half-life (87 yrs)

• An array of thermocouples convert the heat energy to electricity via the Seebeck effect.

• Units typically produce a few 100 s of watts for 25 years.

• Used for remote, unmanned installations– Spacecraft, satellites, polar lighthouses,

navigation beacons, pacemakers (in the past)

Radioactive decay

• Every unstable nucleus has an equal probability of decaying in a second, (the ‘decay constant’)

• Consider a sample containing N0 nuclei at time t=0:– N is the number of undecayed nuclei remaining after

a time t– t is a time interval

• The number of nuclei decaying in a time t is given by: tNN

Radioactive decay

• Exponential decay, like capacitor discharge, water running out of a hole, etc…

• Number of unstable nuclei falls by a fixed proportion in a fixed time period

• Animation here

teNN

NANt

N

tNN

0 gives Nfor thissolving

and , so

Radioactive decay

• Example:– The decay constant for caesium-137 is

7.3x10-10 s–1. Calculate:• The number of atoms present in a sample with an

activity of 2.0 × 105 Bq• The activity of the sample after 30 years

000

0

where,

:so,

NAeAA

eNNt

t

2.7 × 1014

1.0 × 105 Bq

The decay constant

• is the probability of an individual nucleus decaying per second.

• When t = 1/, the activity has fallen to 1/e (~37%) of its initial value.

693.02ln so

2ln5.0ln

0.5 and

o ,

2/1

2/1

0

0

2/1

T

T

eeN

N

seNN

Tt

t

Decay graphs

• Half-life can be read off a graph as the time when N=N0/2

• 1/ can be read off a graph as the time when N=N0/e

• and N0 can also be determined from a ln graph

tNN

eNN t

0

0

lnln

Gradient = -Intercept = ln N0

Dangers of radiation

• Ionising radiation is hazardous to living cells. It can:– Destroy cell membranes, killing cells

– Damage vital molecules such as DNA, possibly leading to:

• Uncontrolled cell division (cancer)• Genetic mutation in sex cells

• These can impact the health of the affected organism and its offspring.

• There is no “safe” dose of radiation– But the higher the exposure the greater the risk

Radiation dose• Radiation dose is measured in

Sieverts (or milliSieverts)– Unit accounts for type and amount

of radiation given

• UK average annual dose2.6 mSv

• The higher the dose, the higher the chances of harm (but there are no guarantees!)– up to 500 mSv: no noticeable

symptoms– 500–1000 mSv: light radiation

poisoning– 3000 mSv: severe radiation

poisoning– > 6000 mSv: always fatal

People at risk from radiation

• Hospital radiologists• Nuclear workers• Pilots and flight crew• Some miners• Industrial radiation

workers

• Exposure is regularly monitored

• Exposure is kept as low as reasonably achievable (ALARA)

• Exposure time is adjusted to ensure annual dose is within accepted levels

Background Radiation

Background radiation – (mostly) harmless!

Correcting for background radiation

• A radiation detector does not distinguish between background and other radiation.

• The background count rate can be measured by simply leaving the detector running for some time away from any obvious sources.

• Any experimental measurement of activity for a source then needs to have this background count rate subtracted to calculate the “true” count rate from the source.

Safety precautions

• Radioactive materials should be:– Stored in lead-lined containers.

• Thick enough to reduce radiation to background levels

• Gases, Liquids and powders should be in sealed containers to avoid ingestion, inhalation or skin contact

– Kept as far from the body as possible• Use tongs, gloves or handling robots to stay out of

range of and and reduce intensity

– Used as quickly as possible• Minimising dose

Uses of radioisotopes• The usual GCSE ones:

– Thickness monitoring

– Imaging (gamma camera)

– Treating cancer • irradiation and contamination

– Sterilisation (seal then irradiate, )• Food• Surgical instruments

Carbon dating

• Half-life of C-14 is 5570 yrs

Argon dating

• Radioactive potassium, “frozen” into rocks when they cool, decays:

• The decay producing Ca is 8 times more likely than the decay producing Ar

• There is no Ar in the rocks when they solidify

• The effective half-life is 1250 My.

e

e

AreK

CaK

4018

01

4019

4020

01

4019

Argon dating

• For every N atoms of K-40 now present, if there is 1 Ar atom present there must have been N+9 K-40 atoms originally.

• Knowing N0, N and T1/2 (or ), we can calculate t using

e

e

AreK

CaK

4018

01

4019

4020

01

4019

8 times more likely

teNN 0

Radioactive tracers

• Radioactive isotopes are chemically identical to their stable cousins, but can be detected.

• A radioactive tracer is introduced to the system of interest and allowed to circulate.

• Information is revealed by where the radioactive isotopes end up.

• Generally want (or ) emitters• See table on p.170

Mass and Energy

• Mass and energy are related:

• According to Einstein, mass is just another form of energy.

• Principle of conservation of mass is therefore just an extension of the principle of conservation of energy.

2mcE

Energy changes in reactions

• Nuclear reactions involve significant changes in mass

• This “lost” mass is transferred to the products as kinetic energy

• Energy released Q=mc2

– In decay, energy shared between nucleus and a particle in inverse proportion to their masses

– In decay, energy is shared between particle and neutrino in varying proportions

• If m=1u, E=931.3 MeV (see worked eg p. 183)

• Now try SQs p. 184

Proof?

Binding Energy

• Unified atomic mass constant, u– u=1.66x10-27 kg (12C has mass 12u, by

definition)

• Mass of a proton=1.0073u• Mass of a neutron=1.0087u• Calculate the mass of an atom of• Measured mass of He is 4.0026u• So where is the “missing mass”?• What is the binding energy released when

a He atom forms?

He42

Binding Energy

• “The binding energy of the nucleus is the work that must be done to separate it into its constituent protons and neutrons”.– i.e. equal to the energy released when the strong

nuclear force did work forming the nucleus

• The release of binding energy on nuclear formation results in a mass defect.– m=Zmp+(A-Z)mn-Mnuc

– Binding energy=mc2

– Hint: if you are given the mass of an atom, don’t forget to subtract Zme

Element Mass of Nuclear Binding Binding Energy nucleons Mass Energy per Nucleon (u) (u) (MeV) (MeV) Deuterium 2.01594 2.01355 2.23 1.12 Helium 4 4.03188 4.00151 28.29 7.07 Lithium 7 7.05649 7.01336 40.15 5.74 Beryllium 9 9.07243 9.00999 58.13 6.46 Iron 56 56.44913 55.92069 492.24 8.79 Silver 107 107.86187 106.87934 915.23 8.55 Iodine 127 128.02684 126.87544 1072.53 8.45 Lead 206 207.67109 205.92952 1622.27 7.88 Polonium 210 211.70297 209.93683 1645.16 7.83

Uranium 235 236.90849 234.99351 1783.80 7.59 Uranium 238 239.93448 238.00037 1801.63 7.57

element nuclear mass (u) Zdeuterium 2.01355 1helium 4 4.00151 2lithium 7 7.01336 3beryllium 9 9.00999 4iron 56 55.92069 26silver 107 106.87934 47iodine 127 126.87544 53lead 206 205.92952 82polonium 210 209.93683 84uranium 235 234.99351 92uranium 238 238.00037 92

proton mass = 1.67262158 × 10–27 kgneutron mass = 1.67492729(28) × 10–27 kg1 amu = 1 u = 1.66053873 × 10–27 kgc = 2.99792458 × 108 ms–1

BE/nucleon = c2m/A=c2(Zmp+(A–Z)mn–Mnuc)/A

Binding energy/nucleon curve

• binding energy/nucleon is the average work done per nucleon to break up a nucleus into constituent particles– A measure of

nuclear stability

Incr

easi

ng s

tabi

lity

fusion fission

Binding energy/nucleon curve

• From the curve, estimate the energy released when:– 235U splits in

two– Two 3He fuse

fusion fission

Nuclear fission• From the binding energy curve, we can see

that energy can be released if heavy nuclei split into lighter ones.

• This can be induced by the absorption of a neutron.– If fast neutrons are needed to provide extra energy

the material is said to be fissionable– If slow neutrons can induce fission the material is

said to be fissile• U-235 and Pu-239 are the only fissile nuclei, according

to your text book (not actually true)

Uranium 235 fission

• Can fission spontaneously, but this is rare.

• Usually induced by the absorption of a neutron

• The nucleus splits into two large particles (see graph) and 2 or 3 neutrons

• ~200 MeV of energy released per fission

Chain reaction

• The fission neutrons released can collide with other fissile nuclei and trigger further fission – a chain reaction

• If, on average, each fission triggers one further fission we have a self-sustaining chain reaction

• If each fission triggers more than one further fission we have a runaway chain reaction

applet

Controlled chain reaction

• Uncontrolled chain reaction – explosion

• Controlled chain reaction – each fission causes one more fission. – Steady release

of energy.To control the rate of energy release we need to control how many neutrons there are

Uncontrolled chain reaction

Uranium

Fission product

neutron

Controlled chain reaction

Uranium

Fission product

Neutron

Control rod

An electricity generation station

• In a conventional power station water is heated by burning fossil fuel

• In a nuclear power station water is heated by energy released during nuclear fission

The Chimney has gone – no CO2!

But nuclear waste is generated...

Nuclear Reactor• Pressurised water reactor (PWR)

– What does pressure do to the water?– Increase the boiling point

• The water circulating through the reactor core is bombarded with neutrons and becomes radioactive. It is kept in a closed circuit.• The water to which the energy is transferred in the heat exchanger may be irradiated as it passes through, but it does not become radioactive and is safe.

Nuclear fuels

• Natural uranium contains <1% U-235

• To make a viable fuel it must be enriched to ~3%

• Plutonium-239 is a by-product of Uranium fission. It can be obtained by re-processing spent nuclear fuel.

• Pu-239 can be used as a nuclear fuel, but not in a conventional reactor.

Reactor components

• Fuel rods– Contain pellets of

Uranium oxide– U-235 content has been

enriched from ~0.7% to ~3%

– Rods made of zirconium alloy

• Resistant to corrosion• “transparent” to neutrons

– Core may contain up to 8,000 fuel rods

Reactor components

• Control rods– Made of silver-indium-cadmium

alloys, or boron– Have a high neutron capture

cross-section– Are moved in and out of the core

to absorb more or fewer neutrons and hence control the rate of the chain reaction

Neutron Moderator

• Fast neutrons from fission are not readily absorbed by U-235, but slower neutrons are

• A moderator reduces the KE of fast neutrons through multiple collisions– A good moderator should be of comparable

mass to a neutron for efficient energy transfer– It should also be a poor absorber of neutrons

• Water and graphite are the most common

Radioactive waste• Nuclear power produces radioactive

waste, some with extremely long half-lives– High, intermediate and low level

Three categories of waste

* A nuclear reactor produces about 3m3 of HLW per year

Category

(quantity /m3/yr worldwide)

Typical composition Storage method

Low level

(150,000)

negligible

Protective clothing, medical waste, building materials

Compacted in drums and stored securely on surface

Intermediate level

(75,000)

10% of total radioactivity

Fuel cladding, filter materials, decommissioned reactor parts, decayed high level waste

Cut up, packed in cement-filled drums and stored securely in surface buildings

High level

(2,000)*

90% of total radioactivity

Spent fuel rods Vitrified and stored securely underwater (to cool) in stainless steel cylinders

Nuclear fusion

• If two small nuclei collide with enough energy they fuse, to produce a new nucleus

• When this happens a large amount of energy is released– This is what makes stars (including our Sun)

shine

• For this to happen the nuclei must be moving very fast– High temperature (~15 million K)

• plasma

– High density (~10,000 x air)

Hydrogen Fusion•Proton-Proton Process

HHHeHeHe

HeHH

eHHH

11

11

42

32

32

32

21

11

01

21

11

11

ν

Hydrogen Fusion

•Step 1: Deuterium formation

ν eHHH 01

21

11

11

Hydrogen Fusion

•Step 2: Deuterium/proton fusion

HeHH 32

21

11

Hydrogen Fusion

•Step3: Helium fusion

HHHeHeHe 11

11

42

32

32

The fusion chain

Fusion reactors

• Mostly try to fuse 2H and 3H• The light nuclei must be very

hot before fusion can take place.– This is done with a very high

electric current

• The plasma must be contained so it doesn’t touch the reactor walls– This is done with magnetic fields

• So far a commercial fusion reactor has not been built.

Practical fusion

• It is very difficult to recreate the conditions necessary to sustain fusion reactions on Earth, but it would be great if we could!– Potentially huge amounts of energy available– Plentiful supply of fuel (from sea water)– Non-radioactive waste products– No greenhouse gases– No chain reaction (so no danger of runaway)

• Research continues…• Now do the end-of-chapter questions