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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