Subject: A-level Physics Topic: Nuclear – types of radiation Year Group: 13

Rutherford’s model of the atom α, β and 𝛾 radiation Key Vocabulary

1 Rutherford fired alpha 1 Alpha Consists of 2 Stopped by paper Range in air 1 Atomic The number of protons in nucleus.
particles at a thin (𝛼) protons and and/or skin. is a few cm. (proton)
sheet of gold foil in a vacuum. 2 neutrons. number
It was in a 2 Beta It is an Stopped by thin Range in air
vacuum to prevent alpha 2 Mass The number of protons and neutrons in
(𝛽) electron. metal sheet. is several
particles been m. (nucleon) nucleus.
absorbed by the air. number
3 Gamma It is high Intensity reduced Ten to
2 The gold foil must be thin to prevent the alpha particles been (𝛾) frequency EM by ½ by 5 cm of hundreds of 3 Isotope Atoms of same element with different
absorbed by the gold and so that they are only scattered radiation. concrete or 1 cm m. numbers of neutrons.
of lead.
once. 4 Background Nuclear radiation that is ever present.
4 Alpha is the most ionising, gamma is the least. radiation Sources include: radon, rocks, cosmic
3 Observation: Explanation:
1. Most alpha particles straight 1. Nuclear radius much rays, nuclear fall out and medicine.
5 Alpha and beta deflect in opposite directions by electric
through the foil with little or smaller than atomic radius. 5 Avogadro The number of particles in one mole of a
and magnetic fields as they have opposite charges.
no deflection. 2. Nucleus is positively constant substance. (6.02 x 1023 particles)
2. Some alpha particles charged and most of mass 6 Beta deflects more than alpha as it is lighter.
suffered large of atom is contained in 6 Mole The amount of substance that contains
deflection/backscattering. nucleus. 7 Gamma is not deflected by magnetic or electric 6.02 x 1023 particles.
fields as it has no charge.
7 Molar mass The mass of one mole of an element or
Detecting radiation and safety compound.
Medical uses of α, β and 𝛾
1 A Geiger-Muller (GM) tube is a device that registers a pulse
of electricity each time an ionising particle enters it. 1 Technetium-99 (𝛾 source) is used as a tracer to make soft Uses of α, β and 𝛾 radiation
tissues show up through medical imaging processes. The tracer is
2 The GM tube is connected to a digital counter, which keeps either injected or ingested and a radiographer positions a 1 Uses of beta radiation To monitor and control the
detector outside the body which can produce a picture of the thickness of aluminium foil, paper
count of the number of ionising particles entering the tube.
patient’s internal organs. Changes in the amount of and steel.
3 When measuring the count rate coming from a source it is gamma emitted from different parts would indicate how well the If the material is too thick the
isotopes are flowing. count rate will fall and the rollers
necessary to account for background radiation by measuring
and subtracting a count rate for background radiation. This will be forced closer together.
2 Technetium-99 is used as it only emits γ rays meaning it can be
If the material is too thin the
gives you the corrected count rate. detected outside the body and since it is the least ionising it
count rate will increase and the
causes little damage. It has a short enough half-life and will not
4 When handling radioactive sources: rollers will be forced apart.
remain active in the body after use. But its half life is long enough
•Always handle sources with tongs to remain active during diagnosis. 2 𝛾 radiation is used to sterilise medical equipment as it is the most
•Point the sources away from your body (and not at any penetrating meaning it can irradiate all sides of the equipment and
3 Treating cancer. Tiny amounts of radium-233 (α source) are
anybody else) equipment can be sterilised whilst in its packaging.
injected into tumours to directly kill cancer cells. Iodine-131 (β
•Fix the source in a holder which is not adjacent to where source) is used to treat thyroid cancer. The cancer cells absorb 3 Gamma emitters are also used as industrial tracers. E.g. a small
your body will be when you take measurements radiation from the material and receive a high dose of energy. amount of radioactive gas can be added to a pipeline system. By
•Replace sources in lead-lined containers as soon as possible Doctors must work out the danger to nearby healthy tissue measuring the gamma intensity above the ground leaks can be
•Wash hands when finished before giving this treatment. detected in the pipes.
 Subject: A-level Physics Topic: Nuclear - radioactivity Year Group: 13
Inverse square law (including required practical) Radioactive decay Key equations
1 For gamma radiation … 1 An unstable nucleus attempts to become stable by emitting
The intensity decreases by a factor of one radiation. The decay is random. 1 Inverse square law 𝐼∝
1
OR I=
𝑘
𝑥2 𝑥2
over the square of the distance, r, from
the source. For example, doubling the 2 Radioactive decay is exponential. This means a quantity
distance from the source decreases decreases by a constant factor in equal intervals of time. 2 Activity Δ𝑁
𝐴 = 𝜆𝑁 = −
intensity by a factor of four. Δ𝑡
3 One way to prove data is
2 Use this set-up exponential is to prove there is a 3 Radioactive decay 𝑁 = 𝑁𝑜 𝑒 −𝜆𝑡
to verify the inverse constant ratio property as shown
𝐴 = 𝐴𝑜 𝑒 −𝜆𝑡
square law from here. Or plot a graph of
ln (data) on the y-axis against t 𝐶 = 𝐶0 𝑒 −𝜆𝑡
gamma
radiation. e.g. ln (A) against t. If a straight
4 Half-life 𝑙𝑛2
line is produced the data is 𝑇1ൗ =
exponential. 2 𝜆

3 Method: 4 A graph of activity against

a) Use a GM tube connected to a counter to measure the count
rate in the room with no radioactive sources present. This is
time can be used to Key Vocabulary
determine half-life.
your background count rate. 1 Intensity The radiation energy passing through a
Half the initial activity. Read
b) Using a metre ruler place your gamma source 5 cm from the
across from this to the line unit area per second.
GM tube and measure the count rate.
c) Calculate the corrected count rate by subtracting the of best fit and then down to
2 Inverse The intensity decreases by a factor of
background count rate from your count rate at this distance. the time axis. This should
square law one over the square of the distance
d) Repeat for a range of distances. give you the half-life.
e) Plot a graph of corrected count rate against 1/x 2. This will be a
from the source.
To check it is correct repeat
straight line that passes through the origin if the inverse square the procedure by halving the 3 Activity The number of decays per second.
law is followed. activity again.
Do this several times and 4 Becquerel Unit of activity. I Bq is equal to 1 decay
Radioactive dating calculate an average half-life. per second.
The gradient of ln(A) against
1 Carbon dating is used to data artefacts that are made of organic
5 Decay The probability of an individual nucleus
t
material (things that were once living). constant of a particular radioisotope decaying
equals –λ.
per second.
2 By comparing the amount of C-14 present now in a sample with the
6 Half-life The time taken for the activity of a
amount of C-14 likely to have been in the sample when it was alive,
the time that has passed since the sample died can be determined.
Decay equations sample to halve OR time taken for half
the radioactive nuclei to decay.
3 Modern carbon dating methods use accelerator mass spectrometry 1 𝑵 = 𝑵𝟎 𝒆−𝝀𝒕 You need to be able to rearrange for t and λ.
to measure the ratio of C-14 to C-12 directly. 𝑁 7 Corrected Counts per second minus background
ln = −𝜆𝑡
𝑁0 count rate counts per second.
4 It is unreliable if the sample is less than 200 years old because it is
difficult to measure accurately the small change in the ratio of C-14 2 If the decay constant is in s-1 time needs to be in seconds. If 8 Carbon A method of dating once living artefacts
to C-12. decay constant is in min-1 time needs to be in min. dating containing carbon by comparing the
ratio of carbon-12 to carbon-14 atoms
5 It is unreliable is the sample is more than 60 000 years old because 3 Exam questions will often say things like the activity falls to 85%
the activity would be very small compared to background/the ratio of of its initial value in a 10 seconds, calculate λ. In this case in a sample. Suitable for dating artefacts
C-14 to C-12 is too small. recognise that A/Ao = 0.85. between 200 and 60 000 years old.
 Subject: A-level Physics Topic: Nuclear – unstable nuclei Year Group: 13
Nuclear radius Decay equations Decay graphs
1 Nuclear radii are approximately 10-15 to 10-14 m. 1 Alpha decay occurs in only A graph which nuclei decay
1 Alpha
the most heavy nuclei. by α, β- and β+
2 The nuclear radius, R, is given by the equation R = R0A1/3 where R0 Beta-minus decay occurs in
is a constant equal to the radius of one nucleon (usually = 1.05 fm) An α particle (He nucleus) is emitted from the nucleus.
nuclei with too many
and A is nucleon number (not activity as for most of this unit). neutrons
2 Beta
minus (neutron rich nuclei).
3 The equation has been confirmed experimentally using 2 methods.
A neutron changes into a proton, an electron and an Beta-plus decay occurs in
4 Closest approach method When an α particle makes a antineutrino. The proton remains in the nucleus, the nuclei with too many
electron and neutrino are emitted. protons.
head on collision with the
nucleus it is repelled backwards Electron capture occurs in
3 Beta plus
due to electrostatic repulsion. proton rich nuclei.
At the distance of closest A proton changes into a neutron, a positron and a
approach (d) the α particle is neutrino. The neutron remains in the nucleus but the
2 You need to be able to show
stationary. All its kinetic energy positron and neutrino are emitted.
decays on graphs such as the N
has been changed to electric
𝑄𝑞 4 Electron one to the right. The parent
EK = EP = potential energy. If you know
4𝜋𝜀0 𝑑 capture nucleus here has a proton
the initial EK of the α particle
The nucleus absorbs one of its inner orbital electrons, number of 84 and a neutron
you can solve for d. resulting in a proton changing into a neutron and an number of 132. Often several
electron neutrino been emitted. An outer orbital decays are required for the
5 Electron diffraction method A beam of high energy e- is fired electron will also fall down an energy level to replace the
at a thin solid sample of an absorbed electron resulting in the emission of an X-ray
nucleus to become stable as Z
element. A detector measures this shows.
photon.
the number of e- scattered
3 Initially it undergoes an alpha decay reducing both the proton
through different. The angle of
and neutron number by 2. Then it undergoes a beta-minus
the first diffraction minimum is Stable nuclei decay which increase Z by 1 an decreases N by 1. And so on.
given by the equation to the left
allowing R to be determined. 1 The graph below shows 4 Use arrows to show if N and Z are increasing or decreasing and
neutron number, N, versus always check the y-axis label to see if it is neutron number or
proton number, Z, for stable mass number as either can be used.
Nuclear excited states nuclei.
If asked to draw this graph in
1 After alpha and beta decays the daughter nucleus can be left in an an exam make sure: Key equations
excited state. To return to its ground state it emits a gamma photon. 1. line passes through N =
10/11 when Z = 10 and N 1 Nuclear radius 𝑅 = 𝑅0 𝐴1/3
2 Here radium-226 is increases as
undergoing alpha decay. Z increases.
6.2 % of the time this results 2. N = 115 → 125 when Z = Key Vocabulary
80 and that the graph bends
in the daughter nucleus been upwards. 1 Metastable An excited nucleus that returns to its ground
created in an excited state. state with a half-life longer than 1 ns. To show
To return to its ground 2 In stable nuclei the electrostatic force pushing the nucleus apart that a nucleus is metastable we put a m after its
state it emits a gamma is balanced by the strong nuclear force pulling it in. mass number e.g. barium-137m.
photon with energy 0.18
3 If nuclei are unstable they can emit alpha, beta and gamma 2 Parent The nucleus which undergoes a decay event to
MeV. Therefore radium-226 nucleus produce one or more daughter nuclei.
radiation in an attempt to balance these forces.
emits alpha particles
of two distinct energies, 3 Daughter The nucleus formed from a radioactive decay
4.78 and 4.60 MeV. nucleus event.
 Subject: A-level Physics Topic: Nuclear – nuclear energy Year Group: 13
E = mc2 Fission and fusion Key equations
1 The mass of an object is a measure of its energy content. 1 Fusion: small nuclei join together, 1
releasing energy.
2 If energy is transferred to an object its mass changes as mass
Energy (J) 𝐸 = 𝑚𝑐 2
can be converted into energy and vice versa.
3 When a nucleus decays energy is released (either gamma photons or 2
Energy (MeV) E = mass difference in u x
as the kinetic energy of the decay products). 2 Fission: large nuclei split up into smaller
nuclei, releasing energy. Not on data sheet 931.5
4 Since energy is released this means some mass must have been
converted into energy and therefore the mass after a decay should
be less than the mass before.
3 In both cases energy is released because the mass of the Key Vocabulary
5 The difference in mass (called the mass difference) is usually products is less than the mass of the reactants. (The difference
measured in atomic mass units, u. in mass is released as energy.) 1 Atomic 1/12th of the mass of a carbon-12
6 1u = 1/12th mass of a C-12 atom = 1.661 x 10-27 kg = 931.5 MeV. 4 This means the binding energy per nucleon of the products is mass unit atom.
greater than the binding energy per nucleon of the reactants. 1 u = 1.66043 x 10-27 kg.
7 To determine the energy released in a decay determine the mass
difference between the starting and the end nuclei in kg then use E = 5 This condition can only be 2 Binding The energy needed to separate all
mc2 to get an energy in J. OR find the mass difference in u and met by nuclei smaller than
energy of the nucleons in a nucleus.
multiply by 931.5 to get an energy in MeV. iron-56 fusing.
OR by nuclei larger than iron-
56 splitting/undergoing fission. 3 Binding The binding energy of the nucleus
Binding energy energy per divided by the nucleon number.
1 Energy has to be supplied to nucleon
separate the nucleons in a
nucleus because the strong Induced fusion
nuclear force has to be 4 Nuclear The joining together of small
overcome. Since energy has 1 Spontaneous fission is rare. We can induce fission by fusion nuclei.
been supplied the mass must bombarding heavy nuclei with neutrons, making them more
increase. unstable.
5 Nuclear The splitting up of large nuclei into
2 Nuclei with more nucleons have the largest binding energy. But in 2 This unstable nucleus then splits into two smaller nuclei called
fission smaller nuclei.
order to judge how tightly bound a nucleus is we use binding energy fission fragments along with a variable number of neutrons
per nucleon (usually 2 or 3).
6 Fission The atomic fragments left after a
3 If you are asked to draw this 3 fragments large atomic nucleus undergoes
graph in the exam be sure to: fission.
• Give the units for binding 4 This diagram shows how the
neutrons produced in fission
energy per nucleon as MeV. 7 Critical The minimum mass required to
• Have the peak is at 8.7 MeV reactions can go onto create a chain
reaction. mass establish a self-sustaining chain
and nucleon number 56.
• Have a sharp rise from reaction.
origin and moderate fall not
below 2/3 of peak height. 8 Critical Exactly one neutron from each
5 Not every neutron produced will go onto induce another fission
chain fission event is allowed to cause
4 The nucleus with the highest binding energy per nucleon is iron-56. reaction. Some maybe absorbed by a control rod, cladding,
coolant or the neutron could escape from the reactor core. reaction another fission event.
Therefore this is the most tightly bound and most stable nucleus.
 Subject: A-level Physics Topic: Nuclear - reactors Year Group: 13
Nuclear waste Nuclear reactors Key Vocabulary
1 High-level waste 1 The main 1 Fissile A radioactive isotope which is capable
components materials of sustaining a chain reaction.
Examples Spent (used) fuel rods. of a nuclear
reactor. 2 Thermal A slow moving neutron which can be
Radioactivity Highly radioactive. Some will be radioactive neutrons captured by a fissile nucleus.
for thousands of years. Generates a lot of
heat. 3 Fast neutron An energetic neutron produced in
nuclear fission.
Storage Placed in cooling ponds close to the
reactor for a number of years.
The plutonium/uranium is separated to be
recycled. It can be vitrified/made solid into Fuel Coolant
Pyrex glass. Then placed in 1 Fission events generate lots of heat in the reactor core which is
steel/lead/concrete containers to be stored 1 The fuel used in nuclear reactors is either natural uranium (0.7% used to turn water into high pressure steam (to spin a turbine,
deep underground in a geological stable U-235 and 99.3% U-238) or enriched uranium (4% U-235 and to spin a generator and so on).
area. 96% U-238).
2 The coolant that passes through the core, absorbing the heat
2 Intermediate-level waste created by the fission events before transferring it to a
2 It is U-235 that undergoes fission. It is the fissile material.
secondary cooling system where high pressure steam is created.
Examples Cladding that is removed from the outside 3 A movable neutron source rods provides the neutrons required 3 Water and carbon dioxide are commonly used as it needs to be
of the spent fuel rods. for the initial start-up of the reactor. able to be pumped around and have good heat transferring
Radioactivity Lower levels of radioactivity than high level abilities.
4 It is not possible to use all the U-235 in the fuel rods as over
waste and it does not generate enough heat time the U-235 percentage decreases as it undergoes fission and
to require cooling. produces its decay products.
Moderator
Storage Some is stored in vaults and some is put in 5 The fission fragments produced absorb neutrons which means
steel drums which are then encased in there are too few neutrons to maintain the chain reaction. 1 The neutrons produced by fission events have lots of kinetic
concrete and often stored underground. energy and are therefore moving quickly.
Thick concrete/bitumen walls are required 2 U-235 is much more likely to absorb a neutron that is travelling
to shield operators from high levels of slowly (thermal neutrons).
radiation. Spent fuel
3 The moderator (often water or graphite) slows the neutrons
3 Low-level waste produced by fission events down without absorbing them.
1 Fuel from a reactor which is no longer useful and is removed
Examples Contaminated clothing (e.g. protective for reprocessing.
shoes and gloves). Considerable amounts of
low level waste are produced by hospitals. 2 When U-235 undergoes fission it releases neutrons and Control rods
produces fission fragments that are neutron rich.
1 Rods used to control the rate of which fission occurs.
Radioactivity Has much lower levels of radioactivity then
the other types of waste and does not 3 The fission fragments are unstable and so often emit beta and 2 When lowered into the reactor they absorb neutrons slowing
generate heat. gamma radiation. the rate of fission. When raised out, the rate of fission rises.

Storage It is usually compacted to reduce its 4 The spent fuel is very radioactive and generates lots of heat. 3 Contain cadmium or boron.
volume and then stored in steel drums.