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
• a 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 a 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 a 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,
1 d 2
1
D
4

,d 
2
10000n 1 D
10000n
4
• So d≈1/10,000.
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: l=hc/E
• Diffraction pattern is superimposed on the
normal scattering pattern
• First diffraction minimum is at an angle q, where
sinq =0.61l/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
1
that
R  r0 A
3
– 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
Volume proportional to mass, so
nuclear density is constant.
V 
4 3
r0 A
3
Constant nucleon spacing –
suggests strong force is same for
all nucleons
Nuclear Radiation
a – Helium nuclei (2 neutrons and 2 protons)
b – electrons (from the nucleus) (or positrons)
g – photons (energy)
Nuclear Radiation
Properties of nuclear radiation
Cloud chamber observations
• Ionising radiation triggers
the formation of droplets
in a supersaturated
vapour
• a particles
– Straight, radiate from
source
– Same length (energy)
•
b 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,
nhf
I
2
4r
1
I 2
r
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?
4
2
He
14
6
C
40
19
K
238
92
U
Alpha emission
• An alpha particle consists of 2 protons and
2 neutrons
4
– Like a helium nucleus
2
a
• So when an atom undergoes a decay it
loses 2 protons and 2 neutrons
• e.g.,
Mass numbers
Th Ra  a
228
90
224
88
4
2
balance
Charge numbers
balance
Beta– emission
• A b- particle is an electron which comes
0
from a neutron-rich nucleus
– A neutron changes into a proton, and an
electron and an antineutrino are emitted
1
b
• So when an atom undergoes b– decay it
gains 1 proton and loses 1 neutron
• e.g.,
40
19
K  Ca b  e
40
20
0
1
Mass numbers
balance
Charge numbers
balance
Beta+ emission
• A b+ particle is a positron (anti-electron)
0
which comes from a proton nucleus
– A proton changes into a neutron, and a
positron and an neutrino are emitted
1
b
• So when an atom undergoes b+ decay it
gains 1 neutron and loses 1 proton
• eg:
C  B  b  e
11
6
11
5
0
1
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.
40
19
K  e  Ar  e

40
18
Mass numbers
balance
Charge numbers
balance
g radiation produced by
“rearrangement” of nucleus
Energy
released
Same
components
Unstable
Stable
• So no change to the nuclear composition
Now do some practice…
• Fill in the missing parts:
?
?
?
?
a
?
?
?
?
• 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?
• a emitters occur for Z>60 or so.
– They have more neutrons than protons, but just not
enough to overcome Coulomb repulsion.
• b- emitters are on the left of the stability belt.
– Neutron-rich nuclei can redress the balance by
converting neutrons to protons
• b+ 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
b
a
b
Z
Natural radioactive series
U238
Th232
• figures in red are half-lives. Figures in boxes are averages for multiple paths.
So when do you get g?
• Similar to electrons, nucleons
only exist in allowed energy
levels.
• Following the emission of an
a of b 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 g emitter
• For medical imaging applications we want an
isotope which
– Has a reasonably short half-life
– Only emits g 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 a 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, l (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
– Dt is a time interval
• The number of nuclei decaying in a time Dt is
given by:
DN  lNDt
Radioactive decay
1100
1000
900
DN  lNDt
800
700
N
600
500
DN
so
 lN , and A  lN
Dt
 lt
solving this for N gives N  N 0e
400
300
200
100
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
time (s)
• 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
5000
Radioactive decay
N  N 0e
 lt
, so :
lt
A  A0e , where A0  lN 0
• 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
2.7 × 1014
• The activity of the sample after 30 years
1.0 × 105 Bq
The decay constant l
• l is the probability of an individual
nucleus decaying per second.
• When t = 1/l, the activity has fallen to 1/e
(~37%) of its initial value.
N  N 0 e  l t , so
N
 e lt and 0.5  e lT1 / 2
N0
ln 0.5   ln 2  lT1/ 2
so T1/ 2 
ln 2
l

0.693
l
Decay graphs
1100
1000
N  N 0e
ln N  ln N 0  lt
800
700
N
600
500
400
300
200
100
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
4500
5000
time (s)
7.0
6.5
Gradient = -l
Intercept = ln N0
6.0
5.5
ln N
• Half-life can be read off a
graph as the time when
N=N0/2
• 1/l can be read off a
graph as the time when
N=N0/e
• l and N0 can also be
determined from a ln
graph
 lt
900
5.0
4.5
4.0
3.5
3.0
0
500
1000
1500
2000
2500
time (s)
3000
3500
4000
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 dose
2.6 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 g 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 a and b and reduce g 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, g)
• Food
• Surgical instruments
Carbon dating
• Half-life of C-14 is 5570 yrs
Argon dating
• Radioactive potassium, “frozen” into rocks
when they cool, decays:
40
0
40
K

b

19
1
20 Ca  e
40
0
40
19 K  1 e18 Ar  e
• 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.
Argon dating
40
19
40
K 10b  20
Ca  e
8 times more likely
40
K  10e18
Ar  e
• 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 l), we can calculate t
using N  N 0 e  lt
40
19
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 g (or b) emitters
• See table on p.170
Mass and Energy
• Mass and energy are related:
E  mc
2
• 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.
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=Dmc2
– In a decay, energy shared between nucleus and a
particle in inverse proportion to their masses Proof?
– In b decay, energy is shared between b particle
and neutrino in varying proportions
• If Dm=1u, E=931.3 MeV (see worked eg p.
183)
• Now try SQs p. 184
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 24 He
Measured mass of He is 4.0026u
So where is the “missing mass”?
What is the binding energy released when
a He atom forms?
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.
– Dm=Zmp+(A-Z)mn-Mnuc
– Binding energy=Dmc2
– Hint: if you are given the mass of an atom,
don’t forget to subtract Zme
Element
Mass of
nucleons
Deuterium
Helium 4
Lithium 7
Beryllium 9
Iron 56
Silver 107
Iodine 127
Lead 206
Polonium 210
Uranium 235
Uranium 238
2.01594
4.03188
7.05649
9.07243
56.44913
107.86187
128.02684
207.67109
211.70297
236.90849
239.93448
Nuclear
Mass
(u)
2.01355
4.00151
7.01336
9.00999
55.92069
106.87934
126.87544
205.92952
209.93683
234.99351
238.00037
Binding
Energy
(u)
2.23
28.29
40.15
58.13
492.24
915.23
1072.53
1622.27
1645.16
1783.80
1801.63
Binding Energy
per Nucleon
(MeV)
(MeV)
1.12
7.07
5.74
6.46
8.79
8.55
8.45
7.88
7.83
7.59
7.57
proton mass = 1.67262158 × 10–27 kg
neutron mass = 1.67492729(28) × 10–27 kg
1 amu = 1 u = 1.66053873 × 10–27 kg
c = 2.99792458 × 108 ms–1
element
deuterium
helium 4
lithium 7
beryllium 9
iron 56
silver 107
iodine 127
lead 206
polonium 210
uranium 235
uranium 238
BE/nucleon
nuclear mass (u)
2.01355
4.00151
7.01336
9.00999
55.92069
106.87934
126.87544
205.92952
209.93683
234.99351
238.00037
Z
1
2
3
4
26
47
53
82
84
92
92
= c2Dm/A
= c2(Zmp+(A–Z)mn–Mnuc)/A
Binding energy/nucleon curve
Increasing stability
• binding
energy/nucleon
is the average
work done per
nucleon to
break up a
nucleus into
constituent
particles
– A measure of
nuclear stability
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
applet
• 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
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
The Chimney has gone – no CO2!
But nuclear waste is generated...
• 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
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
Category
(quantity /m3/yr
worldwide)
Typical composition
Storage method
Low level
(150,000)
negligible
Protective clothing, medical Compacted in drums and
waste, building materials
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
* A nuclear reactor produces about 3m3 of HLW per year
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
0 
1
1
1
H  H H  e  ν
1
1
H  H He  g
3
2
He  He  He  H  H
1
1
2
1
2
1
3
2
3
2
4
2
1
1
1
1
Hydrogen Fusion
0 
1
H H H e  ν
1
1
1
1
2
1
•Step 1: Deuterium formation
Hydrogen Fusion
H H He  g
1
1
2
1
3
2
•Step 2: Deuterium/proton fusion
Hydrogen Fusion
3
2
He  He He  H H
3
2
•Step3: Helium fusion
4
2
1
1
1
1
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