Nuclear Applications
120 minutes
111 marks
Q1.
(a)
(i)
State two physical features or properties required of the shielding to be placed
around the reactor at a nuclear power station.
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(ii)
Which material is usually used for this purpose?
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(3)
(b)
Describe the effect of the shielding on the
rays, neutrons and neutrinos that reach it
from the core of the reactor. Also explain why the shielding material becomes radioactive
as the reactor ages. You may be awarded marks for the quality of written communication
provided in your answer.
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(4)
(Total 7 marks)
Q2.
(a) With reference to the process of nuclear fusion, explain why energy is released when
two small nuclei join together, and why it is difficult to make two nuclei come together
You may be awarded marks for the quality of written communication in your answer.
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(3)
(b)
A fusion reaction takes place when two deuterium nuclei join, as represented by
mass of 2H nucleus
mass of 3He nucleus
mass of neutron
= 2.01355 u
= 3.01493 u
= 1.00867 u
Calculate
(i)
the mass difference produced when two deuterium nuclei undergo fusion,
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(ii)
the energy released, in J, when this reaction takes place.
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(3)
(Total 6 marks)
Q3.
You may be awarded marks for the quality of written communication provided in your
answers to part (a)
(a)
In the context of an atomic nucleus,
(i)
state what is meant by binding energy, and explain how it arises,
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(ii)
state what is meant by mass difference,
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(iii)
state the relationship between binding energy and mass difference.
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(4)
(b)
Calculate the average binding energy per nucleon, in MeV nucleon–1, of the zinc
nucleus
mass of
.
atom
=
63.92915 u
mass of proton
=
1.00728 u
mass of neutron
=
1.00867 u
mass of electron
=
0.00055 u
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(5)
(c)
Why would you expect the zinc nucleus to be very stable?
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(1)
(Total 10 marks)
Q4.
In a nuclear reactor, uranium nuclei undergo induced fission by thermal neutrons. The
reaction is a self-sustaining chain reaction which requires moderation and has to be controlled.
(a)
Explain the meaning of
(i)
induced fission,
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(ii)
thermal neutrons,
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(iii)
self-sustaining chain reaction.
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(5)
(b)
You may be awarded marks for the quality of written communication provided in your
answer to parts (b)(i) and (b)(ii).
(i)
Explain what is involved in the process of moderation.
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(ii)
Describe how the rate of fission is controlled in a nuclear reactor.
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(7)
(Total 12 marks)
Q5.
(a)
(i)
The mass of a nucleus
is M.
If the mass of a proton is mp, and the mass of a neutron is mn, give an expression for
the mass difference ∆m of this nucleus.
∆m = ...................................................................................................
(ii)
Give an expression for the binding energy per nucleon of this nucleus, taking the
speed of light to be c.
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(2)
(b)
The figure below shows an enlarged portion of a graph indicating how the binding energy
per nucleon of various nuclides varies with their nucleon number.
(i)
State the value of the nucleon number for the nuclides that are most likely to be
stable. Give your reasoning.
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(ii)
When fission of uranium 235 takes place, the nucleus splits into two roughly equal
parts and approximately 200 Me V of energy is released. Use information from the
figure above to justify this figure, explaining how you arrive at your answer.
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(5)
(Total 7 marks)
Q6.
(a)
(i)
Explain why, after a period of use, the fuel rods in a nuclear reactor become
less effective for power production,
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(ii)
more dangerous.
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(3)
(b)
Describe the stages in the handling and processing of spent fuel rods after they have
been removed from a reactor, indicating how the active wastes are dealt with.
You may be awarded marks for the quality of written communication in your answer.
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(5)
(Total 8 marks)
Q7.(a)
When a nucleus of uranium -235 fissions into barium -141 and krypton -92, the change in
mass is 3.1 × 10–28 kg. Calculate how many nuclei must undergo fission in order to release
1.0 J of energy by this reaction.
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(2)
(b)
A nuclear power station produces an electrical output power of 600 MW. If the overall
efficiency of the station is 35%, calculate the decrease in the mass of the fuel rods,
because of the release of energy, during one week of continuous operation.
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(4)
(Total 6 marks)
Q8.The age of an ancient boat may be determined by comparing the radioactive decay of
from living wood with that of wood taken from the ancient boat.
A sample of 3.00 × l023 atoms of carbon is removed for investigation from a block of living wood.
In living wood one in 1012 of the carbon atoms is of the radioactive isotope
adecay constant of 3.84 × 10–12 s–1.
, which has
(a)
What is meant by the decay constant?
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(1)
(b)
Calculate the half-life of
significant figures.
in years, giving your answer to an appropriate number of
1 year = 3.15 × 107 s
answer = ..................................... years
(3)
(c)
Show that the rate of decay of the
atoms in the living wood sample is 1.15 Bq.
(2)
(d)
A sample of 3.00 × 1023 atoms of carbon is removed from a piece of wood taken
from the ancient boat. The rate of decay due to the
Calculate the age of the ancient boat in years.
atoms in this sample is 0.65 Bq.
answer = ............................ years
(3)
(e)
Give two reasons why it is difficult to obtain a reliable age of the ancient boat from the
carbon dating described.
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(2)
(Total 11 marks)
Q9.
(a) In a thermal nuclear reactor, one fission reaction typically releases 2 or 3 neutrons.
Describe and explain how a constant rate of fission is maintained in a reactor by
considering what events or sequence of events may happen to the released neutrons.
The quality of your written communication will be assessed in this question.
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(7)
(b)
Uranium is an α emitter. Explain why spent fuel rods present a greater radiation hazard
than unused uranium fuel rods.
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(3)
(Total 10 marks)
Q10.
(a) In a radioactivity experiment, background radiation is taken into account when taking
corrected count rate readings in a laboratory. One source of background radiation is the
rocks on which the laboratory is built. Give two other sources of background radiation.
source 1 .........................................................................................................
source 2 .........................................................................................................
(1)
(b)
A γ ray detector with a cross-sectional area of 1.5 × 10–3 m2 when facing the source is
placed 0.18 m from the source.
A corrected count rate of 0.62 counts s–1 is recorded.
(i)
Assume the source emits γ rays uniformly in all directions.
Show that the ratio
is about 4 × 10–3.
(2)
(ii)
The γ ray detector detects 1 in 400 of the γ photons incident on the facing surface of
the detector.
Calculate the activity of the source. State an appropriate unit.
answer = ................................... unit ...........................................
(3)
(c)
Calculate the corrected count rate when the detector is moved 0.10 m further from the
source.
answer = .......................... counts s–1
(3)
(Total 9 marks)
Q11.A radioactive source used in a school laboratory is thought to emit α particles and γ radiation.
Describe an experiment that may be used to verify the types of radiation emitted by the source.
The experiment described should allow you to determine how the intensity of radiation varies
with distance in air or with the thickness of suitable absorbers.
Your answer should include:
•
the apparatus you would use and any safety precautions you would take
•
the measurements you would make
•
how the measurements would be used to reach a final decision about the emitted
radiation.
The quality of your written communication will be assessed in your answer.
(Total 6 marks)
Q12.(a)
Describe the changes made inside a nuclear reactor to reduce its power output and explain
the process involved.
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(2)
(b)
State the main source of the highly radioactive waste from a nuclear reactor.
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(1)
(c)
In a nuclear reactor, neutrons are released with high energies. The first few collisions of a
neutron with the moderator transfer sufficient energy to excite nuclei of the moderator.
(i)
Describe and explain the nature of the radiation that may be emitted from an excited
nucleus of the moderator.
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(2)
(ii)
The subsequent collisions of a neutron with the moderator are elastic.
Describe what happens to the neutrons as a result of these subsequent collisions
with the moderator.
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(2)
(Total 7 marks)
Q13.(a)
(i)
Define the atomic mass unit.
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(1)
(ii)
State and explain how the mass of a
nucleus is different from the total mass of
its protons and neutrons when separated.
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(2)
(b)
Explain why nuclei in a star have to be at a high temperature for fusion to take place.
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(3)
(c)
(i)
In massive stars, nuclei of hydrogen
are processed into nuclei of helium
through a series of interactions involving carbon, nitrogen and oxygen called the
CNO cycle.
Complete the nuclear equations below that represent the last two reactions in the
series.
(3)
(ii)
The whole series of reactions is summarised by the following equation.
Calculate the energy, in Me V, that is released.
nuclear mass of
= 4.00150 u
energy ..................................... Me V
(3)
(Total 12 marks)
M1.
(a)
(ii)
(i)
thick
high density
material giving minimal fatigue problems after irradiation
any other sensible property e.g. withstands high temperature
any two (1) (1)
(reinforced) concrete (1)
3
(b)
effect of shielding:
rays - intensity (greatly) reduced (1)
neutrons - some absorption (1)
(or speed or energy reduced by collisions) (1)
neutrinos - very little effect (1)
why shielding becomes radioactive:
neutron absorption by nuclei or atoms (1)
makes nuclei (not particles) neutron rich or unstable (1)
become β– emitters and/or
emitters
max 4
QWC 2
[7]
M2.
(a) mass difference increasesor B.E. (per nucleon) or stability is greater for nucleus after
fusion (1)(greater) mass differenceor increase in B.E. (per nucleon) implies energy
released (1)both nuclei charged positively or have like charges (1)electrostatic
repulsion (1)
max 3
QWC 2
(b)
(i)
Δm (= 2 × (2.01355) – (3.01493 + 1.00867))
= 3.5 × 10–3 u (1) (5.81 × 10–30 kg)
(ii)
ΔE = 3.5 × 10–3 × 931.3 (MeV) (1)
(= 3.26 MeV)
= 3.26 × 106 × 1.6 × 10–19 = 5.22 × 10–13 (J) (1)
3
[6]
M3.
(a)
(i)
energy
separate nucleons (1)
energy associated with the strong force (1)
(ii)
mass of nucleus < total mass of constituent nucleons (1)
Δm is difference between mass of nucleus and total mass
of nucleons (1)
[Δm = Zmp + (A – Z)mn – mnucleus (1) (1)]
Eb = (Δm)c2 (1)
[or Eb is energy equivalent of mass defect using E = mc2]
max 4
QWC 1
(b)
mass of nucleus = 63.92915 – (30 × 0.00055) = 63.91265 (u) (1)
Δm = (30 × 1.00728) + (34 × 1.00867) – 63.91265 (1)
= 0.60053 (u) (1)
Eb = 0.60053 × 931.3 = 559.3 (MeV) (1)
Eb/nucleon =
= 8.74 (MeV/nucleon) (1)
(allow C.E. for Δm and Eb)
5
(c)
nucleus has high value of Eb/nucleon[or is near maximum of Eb/nucleon vs A curve] (1)
1
[10]
M4.
(a)
(i)
splitting of nucleus into two smaller nuclei (1)
brought about by bombardment (1)
(ii)
thermal neutrons have low energies or speeds
(e.g. 0.03 eV) (1)
(iii)
fission reaction gives out neutrons (1)
neutrons (from fission) cause further fissions (1)
self-sustaining when one fission leads to (at least) one
further fission (1)
max 5
(b)
(i)
neutrons from fission are fast (high energy) neutrons
(e.g. 2 MeV) (1)
fission most favourable with low energy neutrons (1)
moderation involves slowing down neutrons (1)
by collision with moderator atoms (1)
large number of collisions required (e.g. 50) (1)
collisions are elastic/k.e. transferred to atoms (1)
suitable moderator material named e.g. graphite, water (1)
moderator must not absorb neutrons (1)
moderator atoms should have (relatively) low mass (1)
QWC 1
(ii)
control involves limiting number of neutrons (1)
excess neutrons absorbed by control rods (1)
suitable control rod material named e.g. boron, cadmium (1)
control rods inserted into reactor to slow reaction rate
(or vice-versa) (1)
max 7
[12]
M5.
(a)
(ii)
(i)
∆m = Zmp + (A – Z)mn – M (1)
binding energy per nucleon =
(1)
2
(b)
(i)
A in range 54 → 64 (1)stability increases as binding energy per nucleon
increases (1)[or binding energy per nucleon is a measure of stability][or large
binding energy per nucleon shows nucleus is difficult tobreak apart]
(ii)
binding energy per nucleon increases from about 7.6 to 8.5 (1)increase of about 0.9
MeV for 235 nucleons (1)hence 210 MeV (≈ 200 MeV) in total (1)
5
[7]
M6.
(a)
(ii)
(i)
amount of (fissionable) uranium (235) in fuel decreases (1)
fission fragments absorb neutrons (1)
fission fragments are radioactive or unstable (1)
emitting β– and γ radiation (1)
some fission fragments have short half-lives or high activities (1)
Max 3
(b)
moved by remote control (1)
placed in cooling ponds (1)
for several months (1)
[or to allow short T1/2 isotopes to decay]
transport precautions, e.g. impact resistant flasks (1)
separation of uranium from active wastes (1)
high level waste stored (as liquid) (1)
[alternative for last two marks:
rods are buried deep underground
at geologically stable site]
storage precautions, e.g. shielded tanks or monitoring (1)
reference to vitrification (1)
Max 5
[8]
M7.(a)
for one reaction ΔE (= Δm c2) = 3.1 × 10–28 × (3.00 x 108)2 (1)= (2.79 × 10–11J)
number of nuclei required =
= 3.5(8) × 1010 (1)
[or equivalent credit for any other valid method]
2
(b)
output power from reactor =
(1714 MW)
(MW) (1)
energy output from fuel rods in one week
= 1.70 × 109 × 24 × 7 × 3600 (1)
(= 1.03 × 1015 J)
(1)
= 1.14 ×10–2 kg (1)
[or equivalent credit for any other valid method]
4
[6]
M8.(a)
probability of decay per unit time/given time period
or fraction of atoms decaying per second
or the rate of radioactive decay is proportional to the number of (unstable)
nuclei
and nuclear decay constant is the constant of proportionality (1)
1
(b)
use of
=
= ln2/3.84 × 10–12 s (1) (1.805 × 1011 s)
= (1.805 × 1011/3.15 × 107) = 5730 y (1)
answer given to 3 sf (1)
3
(c)
number of nuclei = N = 3.00 × 1023 × 1/1012 (1)
(= 3.00 × 1011 nuclei)
(using
)
rate of decay = 3.84 × 10–12 × 3.00 × 1011 (1)
(= 1.15 Bq)
2
(d)
(N = N0e–λt and activity is proportional to the number of nuclei A  N use of
A = A0e–λt)
0.65 = 1.15 ×
(1)
t = 4720 y (1)
3
(e)
the boat may have been made with the wood some time after the tree was
cut down
the background activity is high compared to the observed count rates
the count rates are low or sample size/mass is small or there is statistical
variation in the recorded results
possible contamination
uncertainty in the ratio of carbon-14 in carbon thousands of years ago
any two (1)(1)
2
[11]
M9.
(a) The candidate’s writing should be legible and the spelling,punctuation and
grammar should be sufficiently accurate for themeaning to be clear.
The candidate’s answer will be assessed holistically. The answer will beassigned to one
of three levels according to the following criteria.
High Level (Good to excellent): 5 or 6 marks
The information conveyed by the answer is clearly organised, logical andcoherent, using
appropriate specialist vocabulary correctly. The form andstyle of writing is appropriate to
answer the question.
The candidate can explain the role of the moderator and control rods inmaintaining a
critical condition inside the reactor. The explanation is givenin a clear sequence of events
and the critical condition is defined in terms ofneutrons. To obtain the top mark some
other detail must be included. Suchas, one of the alternative scattering or absorbing
possibilities or appropriatereference to critical mass or detailed description of the feedback
to adjustthe position of the control rods etc.
Intermediate Level (Modest to adequate): 3 or 4 marks
The information conveyed by the answer may be less well organised and
not fully coherent. There is less use of specialist vocabulary, or specialist
vocabulary may be used incorrectly. The form and style of writing is less
appropriate.
The candidate has a clear idea of two of the following:
the role of the moderator, the role of the control rods or can explain the
critical condition.
Low Level (Poor to limited): 1 or 2 marks
The information conveyed by the answer is poorly organised and may not
be relevant or coherent. There is little correct use of specialist vocabulary.
The form and style of writing may be only partly appropriate.
The candidate explains that a released neutron is absorbed by uranium to
cause a further fission. Alternatively the candidate may explain one of the
following:
the role of the moderator, the role of the control rods or can explain the
critical condition.
The explanation expected could include the following events thatcould happen to a
released neutron.
a neutron is slowed by the moderator
taking about 50 collisions to reach thermal speeds
then absorbed by uranium-235 to cause a fission event
one neutron released goes on to cause a further fission is the criticalcondition
a neutron may leave the reactor core without further interaction
a neutron could be absorbed by uranium-238
a neutron could be absorbed by a control rod
a neutron could be scattered by uranium-238
a neutron could be scattered by uranium-235
max 7
(b)
it is easy to stay out of range or easy to contain an α source or ß/γ have
greater range/are more difficult to screen (1)
most (fission fragments) are (more) radioactive/unstable (1)
and are initially most likely to be beta emitters/(which also) emit γ
radiation/are neutron rich/heavy (1)
ionising radiation damages body tissue/is harmful (1)
max 3
[10]
M10.
(a)
any 2 from:
the sun, cosmic rays, radon (in atmosphere), nuclear fallout (from previous
weapon testing), any radioactive leak (may be given by name of incident) nuclear
waste, carbon-14
1
(b)
(i)
(ratio of area of detector to surface area of sphere)
ratio =
0.0037
(0.00368)
2
(ii)
activity = 0.62/(0.00368 × 1/400) give first mark if either factor is used.
67000
Bq accept s-1 or decay/photons/disintegrations s-1 but not counts s-1
(67400 Bq)
3
(c)
(use of the inverse square law)
or calculating k = 0.020 from I = k/x2
0.26 counts s-1
(allow 0.24-0.26)
3
[9]
M11.The mark scheme for this part of the question includes an overall assessment for the Quality of
Written Communication (QWC).
QWC
Descriptor
Mark range
High Level (Good to excellent)
The candidate refers to all the necessary apparatus and records the count-rate at various
distances (or thicknesses of absorber). The background is accounted for and a safety
precaution is taken. The presence of an α source is deduced from the rapid fall in the count rate
at 2 – 5 cm in air. The presence of a ɣ source is deduced from the existence of a count-rate
above background beyond 30 -50 cm in air (or a range in any absorber greater than that of beta
particles, e.g. 3 – 6 mm in Al) or from the intensity in air falling as an inverse square of distance
or from an exponential fall with the thickness of a material e.g. lead. The information should be
well organised using appropriate specialist vocabulary. There should only be one or two spelling
or grammatical errors for this mark.
If more than one source is used or a different experiment than the
question set is answered limit the mark to 4
5-6
Intermediate Level (Modest to adequate)
The candidate refers to all the necessary apparatus and records the count-rate at different
distances (or thicknesses of absorber). A safety precaution is stated. The presence of an α
source is deduced from the rapid fall in the count rate at 2 – 5 cm in air and the ɣ source is
deduced from the existence of a count-rate beyond 30 -50 cm in air (or appropriate range in any
absorber, e.g. 3 -6 mm in Al). Some safety aspect is described. One other aspect of the
experiment is given such as the background. The grammar and spelling may have a few
shortcomings but the ideas must be clear.
To get an idea of where to place candidate look for 6 items:
1.Background which must be used in some way either for a
comparison or subtracted appropriately
2.Recording some data with a named instrument
3-4
Low Level (Poor to limited)
The candidate describes recording some results at different distances (or thicknesses of
absorber) and gives some indication of how the presence of α or ɣ may be deduced from their
range. Some attempt is made to cover another aspect of the experiment, which might be safety
or background. There may be many grammatical and spelling errors and the information may be
poorly organised.
3.Safety reference appropriate to a school setting – not lead lined
gown for example
4.Record data with more than one absorber or distances
5.α source determined from results taken
6.ɣ source determined
1-2
The description expected in a competent answer should include a coherent selection of
the following points.
apparatus: source, lead screen, ruler, ɣ ray and α particle detector such as a Geiger Muller
tube, rate-meter or counter and stopwatch, named absorber of varying thicknesses may be
used.
safety: examples include, do not have source out of storage longer than necessary, use long
tongs, use a lead screen between source and experimenter.
measurements: with no source present switch on the counter for a fixed period measured by the
stopwatch and record the number of counts or record the rate-meter reading
with the source present measure and record the distance between the source and detector (or
thickness of absorber)
then switch on the counter for a fixed period measured by the stopwatch and record the number
of counts or record the rate-meter reading
repeat the readings for different distances (or thicknesses of absorber).
from results taken
this is a harder mark to achieve
it may involve establishing an inverse square fall in intensity in air
or an exponential fall using thicknesses of lead
if a continuous distribution is not used an absorber or distance in
air that would just eliminate ɣ (30-50cm air / 3-6mm Al) must be
used with and without the source being present or compared to
background
use of measurements:
for each count find the rate by dividing by the time if a rate-meter was not used
subtract the background count-rate from each measured count-rate to obtain the corrected
count-rate
longer recording times may be used at longer distances (or thickness of absorber).
plot a graph of (corrected) count-rate against distance (or thickness of absorber) or refer to
tabulated values
plot a graph of (corrected) count-rate against reciprocal of distance squared or equivalent linear
graph to show inverse square relationship in air
analysis:
the presence of an α source is shown by a rapid fall in the (corrected) count-rate when the
source detector distance is between 2 – 5 cm in air
the presence of a ɣ source is shown if the corrected count-rate is still present when the source
detector distance is greater than 30 cm in air (or at a range beyond that of beta particles in any
other absorber, e.g. 3 mm in Al)
the presence of a ɣ source is best shown by the graph of (corrected) count-rate against
reciprocal of distance squared being a straight line through the origin
6
[6]
M12.(a)
insert control rods (further) into the nuclear core / reactor
a change must be implied for 2 marks
marks by use of (further) or (more)
allow answers that discuss shut down as well as power reduction
which will absorb (more) neutrons (reducing further fission reactions)
If a statement is made that is wrong but not asked for limit the
score to 1 mark (e.g. wrong reference to moderator)
2
(b)
fission fragments / daughter products or spent / used fuel / uranium rods (allow) plutonium
(produced from U-238)
not uranium on its own
1
(c)
(i)
(electromagnetic radiation is emitted)
A reference to α or β loses this first mark
as the energy gaps are large (in a nucleus) as the nucleus de-excites down
discrete energy levels to allow the nucleus to get to the ground level / state
mark for reason
2nd mark must imply energy levels or states
2
(ii)
momentum / kinetic energy is transferred (to the moderator atoms)
or
a neutron slows down / loses kinetic energy (with each collision)
(eventually) reaching speeds associated with thermal random motion or reaches
speeds which can cause fission (owtte)
2
[7]
M13.(a)
(i)
1/12 the mass of an (atom) of
/ carbon−12 / C12
a reference to a nucleus loses the mark
1
(ii)
separated nucleons have a greater mass
(than when inside a nucleus)
an answer starting with ‘its’ implies the nucleus
because of the (binding) energy added to separate the nucleons or energy
isreleased when a nucleus is formed (owtte)
marks are independent
direction of energy flow or work done must be explicit
2
(b)
nuclei need to be close together (owtte) for the Strong Nuclear Force to be involved or for
fusion to take place
e.g. first mark – within the range of the SNF
but the electrostatic / electromagnetic force is repulsive (and tries to prevent this)
(if the temperature is high then) the nuclei have (high) kinetic energy / speed (to overcome
the repulsion)
3rd mark is for a simple link between temperature and speed / KE
3
(c)
(i)
15
give the middle mark easily for any e or β with a + in any position
12
3
(ii)
Δmass = 4 × 1.00728 − 4.00150 − (2 × 9.11 × 10−31 / 1.661 × 10−27)
or
Δmass = {4 × 1.00728 − 4.00150 − 2 × 0.00055}(u)
(4×1.00728=4.02912)
1st mark – correct subtractions in any consistent unit. use of mp =
1.67 × 10−27 kg will gain this mark but will not gain the 2nd as it will
not produce an accurate enough result
Δmass = 0.02652(u)
2nd mark - for calculated value
0.02652u
4.405 × 10−29 kg
3.364 × 10−12 J
Δbinding energy (= 0.02652 × 931.5)
{allow 931.3}
Δbinding energy = 24.7 MeV
3rd mark – conversion to Mev
conversion mark stands alone
award 3 marks for answer provided some working shown - no
working gets 2 marks
(2sf expected)
3
[12]
E1.
This question was intended to give candidates an opportunity to combine their knowledge of
nuclear properties and reactors, covered extensively in Section 13.5 of the specification, with
their knowledge of particle physics from AS Module 1, to produce well-reasoned answers. Some
were able to do so, but most attempts were too superficial.
Whilst the majority knew that the answer to part (a)(ii) was ‘concrete’, not many could assemble
their thoughts sufficiently to suggest ‘thick’ and ‘dense’ in part (a)(i). Vague statements such as
‘should not let any radiation leak out’ were much more prevalent in candidates’ responses;
these were not considered worthy of credit.
The ability of neutrinos to pass through the shielding was often recognised in part (b), but it is a
misconception that the shielding can prevent all ã radiation and all neutrons from escaping. The
failure to use appropriate technical vocabulary was again a telling weakness in many
candidates’ answers. They wrote about γ radiation being slowed down and
eventually stoppedby the shielding, when they should have referred to its intensity being
reduced. The material was thought to become radioactive because it captured the radioactive
particles, which then remained radioactive within the shielding. It was satisfying to see that at
least some of the candidates realised that neutron absorption by nuclei in the shielding would
make them unstable, being neutron-rich, causing them to be β– and γ emitters.
E2.
Candidates familiar with the principles of nuclear fusion could score all three marks in part
(a) without trouble. The main weaknesses in many scripts were caused by a tendency to write
generally about the mass difference of a nucleus rather than specifically about the increase in
mass difference brought about by the fusion of two light nuclei. Arguments phrased in terms of
the increase in binding energy per nucleon conveyed the most convincing answers. When
addressing the second half of the sentence, a large proportion of the candidates had their
attention distracted by concentrating on the need for a high temperature. They would have been
better advised to focus on the basic physical principle of electrostatic repulsion between two
positively charged nuclei. There was also some confusion with effects attributed to the strong
nuclear force.
In part (b) the calculation of mass difference caused few problems, but the conversion of units in
part (b)(ii) was a bigger hurdle. The main errors were forgetting that 1 MeV is 106 eV (which is
1.6 × 10–13 J), and attempting to convert from eV to J by dividing by e instead of multiplying bye.
E3.
Well-prepared candidates were able to score highly throughout this question. However, the
topic of nuclear binding energy continues to be very poorly understood by many students. The
principal obstacle to progress is a failure to appreciate that binding energy is energy that is
released when a nucleus is formed: it is missing energy rather than energy that a nucleus
possesses. When explaining how it arises, examiners expected candidates to associate binding
energy with the work done on the nucleons by the strong force. A few candidates did this, but
far more strayed into aspects tested later in the question, usually by resorting to mass
difference when answering part (i). Some candidates discussed the whole of parts (i) and (ii) as
though these ideas only have a meaning when dealing with fission (or fusion) reactions.
In part (a) (iii), the equation Eb = (Δm)c2 was known reasonably well. To gain the available mark,
examiners were looking for some explanation of the terms to accompany any bald statement of
the more basic E = mc2. A simple statement that 1u is equivalent to 931.3 MeV was not
regarded as worthy of credit.
Full marks were often awarded for the calculation of binding energy per nucleon in part (b).
Apart from arithmetical errors, candidates‘ main problems were failure to account for the
electron masses, and thinking that the binding energy (the penultimate step) is the same as the
binding energy per nucleon (the final step).
Recognition of binding energy per nucleon (rather than just binding energy) as an essential
measure of nuclear stability was the key to success for the single mark in part (c). Some
candidates spotted that 64Zn would be close to 56Fe, and therefore stable, whilst others gave
valuable references to the binding energy per nucleon curve in order to gain the mark.
E4.
This proved to be a high scoring question for most candidates, who showed better
knowledge of fission processes and nuclear reactors than has sometimes been apparent in
previous years. The main failing in part (a) was a tendency to write about chain reactions
generally, instead of chain reactions involving nuclear fission. This meant that some answers
were not sufficiently specific to the fission process. Fewer candidates than usual stated that
thermal neutrons were ones that had been heated up, and very few indeed thought fission to be
induced by electrons.
In part (b), mixed-up understanding of moderation and control was evident in some scripts.
Occasionally this came out in contradictory statements, such as “moderator rods made out of
carbon absorb the energy and reduce the number of neutrons in the reactor”. When explaining
the kinetic energy lost by the colliding neutrons, candidates need to remember that it is
themass of the moderating atoms that is crucial rather than their size. The control aspect
frequently tempted candidates to write obsessively about emergency shutdown (and/or
meltdown) procedures, instead of confining their answers to a description of control for a reactor
in normal operation. However, the majority had quite good knowledge of the main principles
involved in both moderation and control. The mark scheme adopted for part (b) gave a good
reward to those who knew the main facts.
E5.
The responses to part (a) suggested that students have much less difficulty in calculating a
mass difference when using numbers, than when asked to explain what they are doing using
algebra. Answers to part (a) (ii) were particularly disappointing, demonstrating the ongoing
confusion between binding energy and binding energy per nucleon.
Part (b) was often answered competently, with candidates showing a good understanding of the
role of binding energy per nucleon in determining the stability of a nucleus. Data from the graph
was usually extracted successfully to answer part (b) (ii), but some candidates overlooked the
need to do this and therefore made little progress.
E6.
Many answers to part (a), which for full credit required explanations rather than statements,
would have benefited from a more precise use of terminology. In part (a) (i) for example, ‘the
fuel runs out’ is much inferior to ‘the amount of fissionable uranium remaining decreases’. In
part (a) (ii), a mark was awarded for neutron bombardment causing radioactive instability, but
the real reason is that the fission fragments themselves are unstable neutron-rich β and γ
emitters. Furthermore, since some of them have very short half-lives, their activities can be very
high.
In part (b), the treatment and handling of spent fuel rods was often understood very well.
However, the need to use remote control, and to take precautions over the transport of used
material, was commonly overlooked. Credit was given equally to procedures involving
reprocessing and to those where the spent rods are simply buried deep underground in stable
rock formations.
E7.Both parts of this question could be approached by several routes, and examiners were often
challenged to discover the route by which a candidate had arrived at a correct final answer.
There were frequent, and usually unnecessary, unit conversions into u and MeV and then back
into kg and J. Part (a) was answered well by most candidates.
Part (b) required even greater care with the arithmetic and with powers of ten. The meaning of
the efficiency of the power station was not always appreciated, a common error being to
presume that the reactor output would be 210 MW (which is 35% of 600 MW). Candidates who
made this kind of mistake only suffered a one mark penalty provided the remainder of their
solution hung together in terms of the physics involved.
E8.Less than half the candidates could explain the meaning of the decay constant. By contrast almost
all candidates could find the half-life in part (b) and a majority could answer part (c). Some
candidates did not gain credit because they conveniently removed 1012 in their calculation
without showing the division. So lines like, 1.15 × 1012 Bq = 1.15 Bq, were seen. Most
candidates who tackled part (d) using the exponential decay of the activity equation got full
marks. Only a few candidates could not rearrange the equation. By contrast almost all
candidates who tried to use the exponential decay in the number of nuclei got confused. Most
had numbers of nuclei on one side of the equation but activity on the other.
Part (e) did discriminate but only between scoring zero marks or one mark. Very few candidates
attempted two reasons. Most acceptable answers to this question were difficult for the
candidate to express. For example, in question (d) it states that the decay rate due to carbon-14
is 0.65 Bq, indicating it is a corrected count rate. So an answer to part (e) like, ‘the background
can effect the result’, is not acceptable. This is not the same as saying it is difficult to obtain the
results for the sample activity because the background activity is high in comparison. This
example is also ambiguous in that it suggests the surroundings can influence the rate of decay.
Another answer that was not acceptable was, ‘radioactive decay is random so it’s bound to give
false values’. To gain a mark following this line of thought it was necessary to refer to its effect
on the statistics. The most common answers that candidates found easy to express included
the following; the tree died well before the boat was made; or the boat was repaired later in its
life with fresh wood; or that carbon based microbes died in the wood when the boat was rotting
at the end of its useful life.
E9.
This question was a good discriminator. Most candidates, in part (a), knew how the core of
the reactor functions. Some candidates too readily used the wording of the question as their
answer. Others did not refer to neutrons even though this was asked for in the question. One
example of a phrase given by candidates that did not quite answer the question but sounded
reasonable was, ‘the power levels were kept constant by keeping a constant rate of fission
using control rods’. This offers much of what was in the question itself and it does not refer to
neutrons. The quality of the writing was generally good.
Again question (b) was a good discriminator. The majority of candidates were aware that fission
products are normally unstable because they tend to be neutron rich or that they release beta
and gamma rays. Less able candidates thought used fuel meant that they had undergone alpha
emission.
E10.
A majority of students could not give two clear specific sources of background radiation.
The answers given in response to question part (a) were all too often of a general nature and
too vague to be worthy of a mark. For example, ‘power stations’ or ‘the air’. The answers
needed to be clearer statements like, ‘radioactive material leaked from a power station, or radon
gas in the atmosphere. As only one mark was being awarded only one detailed source gained
the mark provided the second point was in some way appropriate even if poorly stated. Part
(b)(i) was a very good discriminator. More able students realised that a comparison of areas
was required to answer the question. Part (b)(ii) was also a good discriminator. Only the top
20% of students used the detection efficiency factor as well as the fraction of gamma rays
hitting the detector to obtain the correct answer. Most used only the 1/400 detection efficiency.
Students were more successful in choosing the correct unit. Part (c) was interesting in that
students either attempted the question successfully or they left this section blank.
E11.On the whole most candidates knew what approach to take and attempted to explain a suitable
experiment. Weak candidates had issues over the language used to answer this question. Often
they would state that the intensity of radiation needs to be calculated rather than a count rate
needs to be recorded. Also they often stated facts instead of describing an experiment. For
example, alpha particles can be stopped by a sheet of paper is a poor substitute for explaining
what data to take and how to interpret the data to arrive at the conclusion that alpha rays are
emitted from the source. Slightly better candidates started to discuss the background radiation
but they did not always carry on to explain how this would be used in the analysis. Safety in the
experiment was usually given but a majority of candidates tended to overstate the precautions
necessary. It was common to see references to remote handling, lead gowns, and keeping
metres away from the source. Only the better candidates could adequately determine that
gamma rays were given out by the source. These either talked about count-rate falling with the
inverse square of distance or they discussed an absorber, which would have eliminated any
beta radiation but still allows some radiation to pass through. The only way to know radiation
passes through is to compare the count-rate with the background radiation. It was this last point
that many candidates missed. Overall candidates seemed to lack planning. They often missed
important considerations and bolted them on at the end. The standard of English still leaves a
lot to be desired. The writing in several cases was virtually illegible and keywords were often
misspelled. Fortunately there were candidates in contrast to this description who performed the
writing task exceedingly well.
E12.Most candidates were fully aware of the function of the control rods in absorbing excess neutrons
and scored well in part (a). Some candidates said too much by explaining the role of the control
rods to absorb neutrons and the moderator to slow neutrons down but then did not make it clear
which reduced the power. The weaker candidates talked about control rods controlling the
reactions without any further explanation.
Part (b) was answered well by most but it was common to give the answer fuel rods rather than
spent fuel rods.
In (c)(i) the most common answer was ‘gamma rays’ but very few then went on to discuss
energy levels. Some of those that did then spoilt their answer by referring to changing electron
levels.
Part (c)(ii) was a very good question to distinguish between the weak and strong candidates.
The weaker candidates focussed on the wording in question concerning elastic collisions. They
interpreted this to mean the neutrons maintain their kinetic energy or momentum during all
subsequent collisions.
E13.Very few candidates knew what the atomic mass unit was. A surprising number thought it was
simply another name for nucleon number. The next choice of candidates in giving the definition
of the atomic mass unit was to give an energy or mass equivalence in J, MeV or kg.
In part (a)(ii) a majority knew that the mass of the nucleus was less than its constituents but too
many simply repeated back the question and said they were different. The explanation of why
they are different was very vague by most candidates. The majority thought it was sufficient to
simply state energy and mass are equivalent.
Part (b) was very discriminating. Only the best candidates scored the 3 marks because for most
there was a lack of appreciation that 3 marks usually equates to 3 points needing to be made in
answering the question. Some of the vague statements made included, ‘it takes a great deal of
energy to get fusion to start’ and many also referred to the need to overcome the SNF rather
than an electrostatic force before nuclei could get close enough to fuse.
Completion of the first equation in (c)(i) was done incorrectly by most because they did not pick
up the fact that the emitted particle must be an anti-lepton. The conservation laws covered in
module PHYA1 were often flouted in answering this question. The second equation was done
correctly by most.
The main feature that came out in (c)(ii) was how disorganised a majority of candidates are in
presenting their work. The consequence of this was that it became very difficult to award marks
for incomplete answers when there was just a jumble of figures on the page. The calculation
was difficult for many because they could not decide which units to work in. The more
successful chose to work in atomic mass units. Even here many thought the mass of the
hydrogen nucleus was 1u. In addition candidates answers often lacked precision leading to
rounding errors by using, for example, 1.67 × 10-27 kg rather than 1.673 × 10-27 kg for the mass of
the proton.
N1.Question source: Legacy Spec A January 2003 Unit 4B Question 4
Description: Shielding a reactor
Marks: 7
Mathematical requirements: None
Topic: Nuclear applications
Type: State/explain/describe
Specification: 5.2.2 Induced fission
N2.Question source: Legacy Spec A June 2003 Unit 4B Question 4
Description: Energy release with fusion
Marks: 6
Mathematical requirements: Decimal and standard form | Substitution | Solve equations
Topic: Nuclear applications
Type: State/explain/numerical
Specification: 5.2.1 Mass and energy
N3.Question source: Legacy Spec A June 2004 Unit 4B Question 3
Description: Binding energy; mass diff; av BE/nucleon Zinc 64
Marks: 10
Mathematical requirements: Substitution | Solve equations
Topic: Nuclear applications
Type: State/explain/numerical
Specification: 5.2.1 Mass and energy
N4.Question source: Legacy Spec A January 2005 Unit 4B Question 5
Description: Fission terms; moderation; reaction rate control
Marks: 12
Mathematical requirements: None
Topic: Nuclear applications
Type: State/explain/describe
Specification: 5.2.2 Induced fission
N5.Question source: Legacy Spec A June 2005 Unit 4B Question 5
Description: Binding energy per nucleon
Marks: 7
Mathematical requirements: Manipulate equations | Substitution | Translate information
Topic: Nuclear applications
Type: State/explain/numerical
Specification: 5.2.1 Mass and energy
N6.Question source: Legacy Spec A January 2006 Unit 4B Question 3
Description: Fuel rods; handling and processing
Marks: 8
Mathematical requirements: None
Topic: Nuclear applications
Type: State/explain/describe
Specification: 5.2.2 Induced fission | 5.2.3 Safety aspects
N7.Specification 7408
Question source:Legacy Spec A June 2006 Unit 4B Question 5
Description: Nuclei - fission; decrease in mass per week
Marks: 6
Maths requirements: Decimal + standard form | Substitution | Solve equations
Maths demand: 2
Topic: Nuclear applications
Type: Structured quantitative
Specification: 3.8.1.6 Mass and energy
Specification 2450
Question source: Legacy Spec A June 2006 Unit 4B Question 5
Description: Nuclei - fission; decrease in mass per week
Marks: 6
Maths requirements: Decimal and standard form | Calculator functions | Substitution | Solve equations
Topic: Nuclear applications
Type: Structured quantitative
Specification: 5.2.1 Mass and energy
N8.Specification 7408
Question source: June 2010 Unit 5 Question 3
Description: Radioactive dating of wood
Marks: 11
Maths requirements: Decimal + standard form | Manipulate equations | Substitution | Solve equations |
Exponential + logarithmic functions
Maths demand: 2
Topic: Nuclear applications
Type: Mostly numerical
Specification: 3.8.1.3 Radioactive decay
Specification 2450
Question source: June 2010 Unit 5 Question 3
Description: Radioactive dating of wood
Marks: 11
Maths requirements: Decimal and standard form | Calculator functions | Manipulate equations |
Substitution | Solve equations
Topic: Nuclear applications
Type: Mostly numerical
Specification: 5.1.4 Nuclear instability
N9.Question source: June 2010 Unit 5 Question 2
Description: Thermal nuclear reactor
Marks: 10
Mathematical requirements: None
Topic: Nuclear applications
Type: Extended writing
Specification: 5.2.2 Induced fission | 5.2.3 Safety aspects
N10.Question source: June 2012 Unit 5 Question 3
Description: Gamma ray detector
Marks: 9
Mathematical requirements: Ratio; fraction; percentage | Manipulate equations | Substitution | Solve
equations | Circumference; area; volume
Topic: Nuclear applications
Type: Mostly numerical
Specification: 5.1.2 alpha/beta/gamma radiation
N11.Question source: June 2013 Unit 5 Question 5
Description: Describe an absorption experiment
Marks: 6
Mathematical requirements: Calculator functions
Topic: Nuclear applications
Type: Extended writing
Specification: 5.1.2 alpha/beta/gamma radiation
N12.Question source: June 2013 Unit 5 Question 2
Description: Processes in a nuclear reactor
Marks: 7
Mathematical requirements: None
Topic: Nuclear applications
Type: State/explain/describe
Specification: 5.2.2 Induced fission
N13.Question source: June 2013 Unit 5 Question 1
Description: Fusion reactions in stars
Marks: 12
Mathematical requirements: Decimal and standard form
Topic: Nuclear applications
Type: State/explain/numerical
Specification: 5.2.1 Mass and energy