1
A rod made from uranium−238 (
U) is placed in the core of a nuclear reactor where it absorbs
free neutrons.
When a nucleus of uranium−238 absorbs a neutron it becomes unstable and decays to
neptunium−239 (
(a)
Np), which in turn decays to plutonium−239 (
Pu).
Write down the nuclear equation that represents the decay of neptunium−239 into
plutonium−239.
(2)
(b)
A sample of the rod is removed from the core and its radiation is monitored from time t = 0
s.
The variation of the activity with time is shown in the graph.
Page 1 of 45
(i)
Show that the decay constant of the sample is about 3.4 × 10–6 s–1.
(2)
(ii)
Assume that the activity shown in the graph comes only from the decay of neptunium.
Estimate the number of neptunium nuclei present in the sample at time t = 5.0 × 105
s.
number of nuclei .....................................................
(1)
(c)
(i)
A chain reaction is maintained in the core of a thermal nuclear reactor that is
operating normally.
Explain what is meant by a chain reaction, naming the materials and particles
involved.
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(2)
Page 2 of 45
(ii)
Explain the purpose of a moderator in a thermal nuclear reactor.
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(2)
(iii)
Substantial shielding around the core protects nearby workers from the most
hazardous radiations. Radiation from the core includes α and β particles, γ rays,
X−rays, neutrons and neutrinos.
Explain why the shielding becomes radioactive.
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(2)
(Total 11 marks)
2
(a)
Explain what is meant by a thermal neutron.
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(2)
Page 3 of 45
(b)
A student sets up the arrangement, shown in the diagram below, to demonstrate the
principle of moderation in a nuclear reactor.
A golf ball of mass 50 g is initially hanging vertically and just touching a hockey ball of mass
150 g. The golf ball is pulled up to the side and released. It has a speed of 1.3 m s−1 when
it collides head-on with the hockey ball. After the collision the balls move in opposite
directions with equal speeds of 0.65 m s−1.
(i)
Calculate the height above its initial position from which the golf ball is released.
Assume that there is no air resistance.
height ................................................. m
(2)
(ii)
Show that momentum is conserved in the collision and that the collision is perfectly
elastic.
(4)
Page 4 of 45
(iii)
Calculate the percentage of the kinetic energy of the golf ball transferred to the
hockey ball during the collision.
percentage transferred ................................................. %
(2)
(iv)
Explain how this demonstration relates to the moderation process in a reactor and
state one way in which the collisions in a reactor differ from the collision in the
demonstration.
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(2)
(v)
Name the substance used as the moderator in a pressurised water reactor (PWR).
...............................................................................................................
(1)
(Total 13 marks)
3
(a)
State what is meant by the binding energy of a nucleus.
........................................................................................................................
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(2)
(b)
(i)
When a
nucleus absorbs a slow-moving neutron and undergoes fission one
possible pair of fission fragments is technetium
and indium
.
Complete the following equation to represent this fission process.
(1)
Page 5 of 45
(ii)
Calculate the energy released, in MeV, when a single
fission in this way.
binding energy per nucleon of
= 7.59 MeV
binding energy per nucleon of
= 8.36 MeV
binding energy per nucleon of
= 8.51 MeV
nucleus undergoes
energy released ..................................... MeV
(3)
(iii)
Calculate the loss of mass when a
nucleus undergoes fission in this way.
loss of mass ......................................... kg
(2)
Page 6 of 45
(c)
(i)
On the figure below sketch a graph of neutron number, N, against proton number, Z,
for stable nuclei.
proton number, Z
(1)
Page 7 of 45
(ii)
With reference to the figure, explain why fission fragments are unstable and explain
what type of radiation they are likely to emit initially.
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(3)
(Total 12 marks)
4
A thermal nuclear reactor is shut down by inserting the control rods fully into the core. Which line,
A to D, shows correctly the effect of this action on the fission neutrons in the reactor?
number of fission
neutrons
A
B
C
D
average kinetic energy
of fission neutrons
reduced
reduced
unchanged
unchanged
reduced
unchanged
reduced
unchanged
(Total 1 mark)
5
The moderator in a nuclear reactor is sometimes made of graphite. What is the purpose of the
graphite?
A
to absorb all the heat produced
B
to decrease the neutron speeds
C
to absorb the α and γ radiations
D
to prevent the reactor from going critical
(Total 1 mark)
Page 8 of 45
6
In a thermal reactor, induced fission is caused by the
nucleus capturing a neutron,
undergoing fission and producing more neutrons. Which one of the following statements is true?
A
To sustain the reaction a large number of neutrons is required per fission.
B
The purpose of the moderator is to absorb all the heat produced.
C
The neutrons required for induced fission of
D
The purpose of the control rods is to slow down neutrons to thermal speeds.
should be slow neutrons.
(Total 1 mark)
7
(a)
(i)
Explain what is meant by the term binding energy for a nucleus.
...............................................................................................................
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(ii)
Sketch on the axes a graph of the average binding energy per nucleon against
nucleon number A, giving approximate values of the scale on each axis.
(5)
(b)
Use your graph to explain why energy is released when a neutron collides with a
nucleus causing fission.
(2)
Page 9 of 45
(c)
Neutrons are released when nuclear fission occurs in
. Some of these neutrons induce
further fission, others are absorbed without further fission and others escape from the
surface of the material. The average number of neutrons released per fission is 2.5, of
which at least one must produce further fission if a chain reaction is to be sustained.
Explain how a chain reaction can occur only if the piece of uranium has a certain minimum
mass (the critical mass).
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(3)
(Total 10 marks)
8
Natural uranium consists of 99.3%
and 0.7%
In many nuclear reactors, the fuel
consists of enriched uranium enclosed in sealed metal containers.
(a)
(i)
Explain what is meant by enriched uranium.
...............................................................................................................
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(ii)
Why is enriched uranium rather than natural uranium used in many nuclear reactors?
...............................................................................................................
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(2)
(b)
(i)
By considering the neutrons involved in the fission process, explain how the rate of
production of heat in a nuclear reactor is controlled.
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Page 10 of 45
(ii)
Explain why all the fuel in a nuclear reactor is not placed in a single fuel rod.
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(5)
(Total 7 marks)
9
(a)
(i)
Complete the equation below which represents the induced fission of a nucleus of
uranium
(ii)
.
The graph shows the binding energy per nucleon plotted against nucleon number A.
Mark on the graph the position of each of the three nuclei in the equation.
Page 11 of 45
(iii)
Hence determine the energy released in the fission process represented by the
equation.
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(6)
(b)
(i)
Use your answer to part (a)(iii) to estimate the energy released when 1.0 kg of
uranium, containing 3% by mass of
, undergoes fission.
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(ii)
Oil releases approximately 50 MJ of heat per kg when it is burned in air. State and
explain one advantage and one disadvantage of using nuclear fuel to produce
electricity.
advantage .............................................................................................
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disadvantage ........................................................................................
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(6)
(Total 12 marks)
Page 12 of 45
10
(a)
Nuclear fission can occur when a neutron is absorbed by a nucleus of uranium-235. An
incomplete equation for a typical fission reaction is given below.
(i)
State the nuclear composition of X.
proton number ......................................................................................
neutron number ....................................................................................
(ii)
Name the element of which X is an isotope.
...............................................................................................................
(3)
(b)
In a small nuclear power plant one fifth of the fission energy is converted into a useful
output power of 10 MW. If the average energy released per fission is 3.2 × 10–11 J,
calculate the number of uranium-235 nuclei which will undergo fission per day.
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(3)
(Total 6 marks)
11
A space probe contains a small fission reactor, fuelled by plutonium, which is designed to
produce an average of 300 W of useful power for 100 years. If the overall efficiency of the reactor
is 10%, calculate the minimum mass of plutonium required.
energy released by the fission of one nucleus of
= 3.2 × 10–11J
Page 13 of 45
the Avogadro constant = 6.0 × 1023 mol–1
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(Total 7 marks)
12
(a)
The unstable uranium nucleus
is produced in a nuclear reactor.
(i)
Complete the equation which shows the formation of
.
(ii)
can decay by nuclear fission in many different ways. Complete the equation
which shows one possible decay channel.
(2)
(b)
Calculate the energy released, in MeV, in the fission reaction.
atomic mass of
= 144.92694 u
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(3)
(Total 5 marks)
Page 14 of 45
13
Artificial radioactive nuclides are manufactured by placing naturally-occurring nuclides in a
nuclear reactor. They are made radioactive in the reactor as a consequence of bombardment by
A
α particles.
B
β particles.
C
protons.
D
neutrons.
(Total 1 mark)
14
The moderator in a nuclear reactor is sometimes made of graphite. What is the purpose of the
graphite?
A
to absorb all the heat produced
B
to decrease the neutron speeds
C
to absorb α and γ radiations
D
to prevent the reactor from going critical
(Total 1 mark)
15
(a)
In the reactor at a nuclear power station, uranium nuclei undergo induced fission with
thermal neutrons. Explain what is meant by each of the terms in italics.
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(3)
(b)
A typical fission reaction in the reactor is represented by
(i)
Calculate N.
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(ii)
How do the neutrons produced by this reaction differ from the initial neutron that goes
into the reaction?
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Page 15 of 45
(iii)
Calculate the energy released in MeV when one uranium nucleus undergoes fission
in this reaction. Use the following data.
mass of neutron
mass of 235U nucleus
mass of 92Kr nucleus
mass of 141Ba nucleus
1 u is equivalent to 931 MeV
= 1.00867 u
= 234.99333 u
= 91.90645 u
= 140.88354 u
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(5)
(Total 8 marks)
16
(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)
Page 16 of 45
(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)
17
Which line, A to D, in the table gives a combination of materials that is commonly used for
moderating, controlling and shielding respectively in a nuclear reactor?
moderating
controlling
shielding
A
graphite
carbon
lead
B
cadmium
carbon
concrete
C
cadmium
boron
lead
D
graphite
boron
concrete
(Total 1 mark)
18
Which one of the following statements is not true about the control rods used in a nuclear
reactor?
A
They must absorb neutrons.
B
They must slow down neutrons to thermal speeds.
C
They must retain their shape at high temperatures.
D
The length of rod in the reactor must be variable.
(Total 1 mark)
19
Why is a moderator required in a thermal nuclear reactor?
A
to prevent overheating of the nuclear core
B
to absorb surplus uranium nuclei
C
to shield the surroundings from gamma radiation
D
to reduce the kinetic energy of fission neutrons
(Total 1 mark)
Page 17 of 45
20
The sodium isotope
Na is a radioactive isotope that can be produced by bombarding the
aluminium isotope Al with neutrons. Which line, A to D, in the table correctly represents the
production of
Na from the aluminium isotope
production
Al and its subsequent decay?
decay
A
B
C
D
(Total 1 mark)
Page 18 of 45
21
The figure below shows the variation in binding energy per nucleon with nucleon number.
(a)
A uranium-235, 235U, nucleus fissions into two approximately equally sized products. Use
data from the graph to show that the energy released as a result of the fission is
approximately 4 × 10–11J.
Show on the graph how you have used the data.
(4)
Page 19 of 45
(b)
Using the data below, show that the energy available from the fusion of two hydrogen-2,2H,
nuclei to make a helium-4,4He, nucleus is approximately 3.7 × 10–12 J.
mass of 2H = 2.0135 u
mass of 4He = 4.0026 u
(4)
(c)
Compare the energy available from the complete fission of 1 kg of uranium-235 with the
energy available from the fusion of 1 kg of hydrogen-2.
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(3)
(d)
Fission and fusion reactions release different amounts of energy. Discuss other reasons
why it would be preferable to use fusion rather than fission for the production of electricity,
assuming that the technical problems associated with fusion could be overcome.
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(2)
(Total 13 marks)
Page 20 of 45
22
The fissile isotope of uranium,
, has been used in some nuclear reactors. It is
normally produced by neutron irradiation of thorium-232. An irradiated thorium nucleus emits a β−
particle to become an isotope of protactinium.
This isotope of protactinium may undergo β− decay to become
(a)
.
Complete the following equation to show the β− decay of protactinium.
Pa →
+
β + ……..
–
(2)
(b)
Two other nuclei, P and Q, can also decay into
P decays by β+ decay to produce
Q decays by α emission to produce
.
.
.
The figure below shows a grid of neutron number against proton number with the
position of the
isotope shown.
On the grid label the positions of the nuclei P and Q.
Page 21 of 45
(2)
(c)
A typical fission reaction in the reactor is represented by
+
(i)
→
+
+ x neutrons
Calculate the number of neutrons, x.
answer = .............................neutrons
(1)
(ii)
Calculate the energy released, in MeV, in the fission reaction above.
mass of neutron = 1.00867 u
mass of
nucleus = 232.98915 u
mass of
nucleus = 90.90368 u
mass of
nucleus = 138.87810 u
answer = ..................................MeV
(3)
(Total 8 marks)
Page 22 of 45
23
For a nuclear reactor in which the fission rate is constant, which one of the following statements
is correct?
A
There is a critical mass of fuel in the reactor.
B
For every fission event, there is, on average, one further fission event.
C
A single neutron is released in every fission event.
D
No neutrons escape from the reactor.
(Total 1 mark)
24
In a nuclear reactor the mean energy produced by each uranium-235 nucleus that undergoes
induced fission is 3.0 × 10–11 J. In one pressurised water reactor, PWR, the fuel rods in the
reactor contain 2.0 × 104 kg of uranium-235 and 40% of the energy produced per second is
converted to 500 MW of electrical output power. It is assumed that all the energy produced in the
reactor core is removed by pressurised water in the coolant system. The pressure of the water is
approximately 150 times greater than normal atmospheric pressure. The water enters the reactor
at a temperature of 275 °C ad leaves at a temperature of 315 °C. Under the operational
conditions of the reactor the mean density of water in the coolant circuit is 730 kg m–3 and the
specific heat capacity of water is approximately 5000 J kg–1 K–1.
normal atmospheric pressure = 1.0 × 105 Pa
molar mass of uranium-235 = 0.235 kg
(a)
The equation below gives one induced fission reaction that takes place in a reactor.
(i)
State the name of the particle represented by X.
...............................................................................................................
(1)
(ii)
State the proton and nucleon numbers represented by p and n.
p ..........................................................
n ..........................................................
(2)
Page 23 of 45
(b)
(i)
Calculate the number of fission reactions that occur in the reactor each second.
number of fission reactions per second ............................................
(2)
(ii)
The reactor fuel rods contain 2.0 × 104 kg of uranium-235. Assume that all this
uranium-235 could be used.
Calculate the maximum time, in years, for which the reactor could operate.
time .........................................................years
(4)
(iii)
Suggest why it is not possible to use all the uranium-235 in the reactor fuel rods.
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(2)
(c)
Calculate the force exerted by the pressurised water on each square centimetre of the wall
of the reactor.
force .........................................................N
(2)
Page 24 of 45
(d)
Calculate, in m3 s–1, the flow rate of the water through the PWR reactor.
You will need to use data from the passage at the beginning of the question.
flow rate ......................................................... m3 s–1
(4)
(e)
In a PWR the cooling water also acts as the moderator in the reactor and boron rods are
used to control the power output. Describe the physical processes that take place in the
moderator and control rods.
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(4)
(Total 21 marks)
Page 25 of 45
Mark schemes
1
Np →
(a)
Pu +
β- +
✓✓
First mark for one anti-neutrino or one beta minus particle in any
form e.g. e-. If subscript and superscripts are given for these they
must be correct but ignore the type of neutrino if indicated.
The second mark is for both particles and the rest of the equation.
Ignore the full sequence if it is shown but the Np to Pu must be
given separately for the mark.
2
(b)
(i)
T1/2 2.0
2.1 × 105 s ✓
then substitute and calculate
λ = ln 2 / T1/2 ✓
T1 / 2 may be determined from graph not starting at zero time.
Look for the correct power of 10 in the half-life ‒ possible AE.
Or
(substitute two points from the graph into A = Aoe-λt)
e.g. 0.77 × 1012 = 4.25 × 1012 exp(-λ×5×105) ✓
then make λ the subject and calculate ✓
(the rearrangement looks like
λ = [ln (Ao / A)] / t
or λ = ‒ [ln (A / Ao )] / t )
Allow the rare alternative of using the time constant of the decay
A = Ao exp (-t / ttc)
from graph ttc = 2.9 3.1 × 105 s✓
λ = 1 / ttc = 3.4 × 10-6 s-1 ✓
No CE is allowed within this question.
both alternatives give
λ = 3.3 3.5 × 10-6 s-1 ✓
For reference
T1/2 = 2.0 × 105 s gives
λ = 3.5 × 10-6 s-1 and
T1/2 = 2.1 × 105 s gives
λ = 3.3 × 10-6 s-1.
2
(ii)
(using A = Nλ
N = 0.77 × 1012 / 3.4 × 10-6 = 2.2(6) × 1017 )
allow 2.2 2.4 × 1017 nuclei ✓
A possible route is find No = Ao / λ
then use N = Noe-λt.
Condone lone answer.
1
Page 26 of 45
(c)
(i)
uranium (‒ 235 captures) a neutron (and splits into 2 smaller nuclei / fission
fragments) releasing more neutrons ✓
First mark for uranium + neutron gives more neutrons.
Ignore which isotope of uranium is used.
(at least one of) these neutrons go on to cause further / more splitting /
fissioning (of uranium‒ 235) ✓
Second mark for released neutron causes more fission.
The word ‘reaction’ may replace ‘fission’ here provided ‘fission /
splitting of uranium’ is given somewhere in the answer.
2
(ii)
Escalate if clip shows critical mass in the question.
the moderator slows down / reduces the kinetic energy of neutrons ✓
so neutrons are absorbed / react / fission (efficiently) by the uranium / fuel ✓
owtte
Possible escalation.
2
(iii)
neutrons are absorbed / collide with (by the nuclei in the shielding) ✓
Second mark is only given if neutrons appear somewhere in the
answer.
converting the nuclei / atoms (of the shielding) into unstable isotopes (owtte)
No neutrons = no marks.
Making it neutron rich implies making them unstable.
2
[11]
2
(a)
ANY 2 from
•
Slow moving neutrons or low (kinetic) energy neutrons
B1
•
(They are in) thermal equilibrium with the moderator /
Are in thermal equilibrium with other material (at a
temperature of about 300 K)
B1
•
Have energies of order of 0.025 eV
•
Have (range of) KE similar to that of a gas at 300 K or
room temperature
2
Page 27 of 45
(b)
(i)
Use of mgh = ½ mv 2 by substitution or rearranges to make
h the subject
PE for use of equation of motion (constant acceleration)
C1
0.086(1) (m) or 0.086(2) (m)
A1
2
(ii)
Correct equation for conservation of momentum
m1u1 (+ m2u2)= m1v1 + m2v2
or states momentum before = momentum after or pbefore= pafter
B1
(Correct clear Manipulation =) 0.065 (+ 0) = − 0.0325 +
0.0975
or −0.065 (+ 0) = 0.0325 − 0.0975 must see signs
Condone non−SI here:
65 (+0) = − 32.5 + 97.5
B1
States initial kinetic energy = final kinetic energy or
States kinetic energy is conserved
Allow equivalent on RHS where masses are summed in
one KE term
B1
(Correct clear Manipulation=) 0.04225 = 0.0105625 +
0.0316875
Or equivalent workings with numbers seen
and 0.04225 = 0.04225 / KE before = KE after
B1
4
Page 28 of 45
(iii)
(Percentage / fraction remaining after 1 collision =) ¼ = 25%
seen
C1
OR
% remaining = 100 × ½ m(1.32 − 0.652)/ ½ m1.32
or hockey ball = 0.0317 and initial ke = 0.04225
or their KE hb / 0.04225 or their KEhb / their KET
75(%)
range
75 to 76
A1
2
(iv)
Demonstrates:
Slowing down / loss of KE of golf ball is like neutrons slowed
down / Neutrons can lose KE by elastic collisions also
B1
Differs:
Collisions in a reactor are not always / rarely head-on
or
KE loss is variable
or
Collisions are not always elastic
or
Ratio of mass of neutron to mass of nucleus is usually much
smaller in a reactor
B1
2
(v)
Water
B1
1
[13]
3
(a)
the amount of energy required to separate a nucleus ✓
into its separate neutrons and protons / nucleons ✓
(or energy released on formation of a nucleus ✓
from its separate neutrons and protons / constituents ✓)
1st mark is for correct energy flow direction
2nd mark is for binding or separating nucleons (nucleus is in the
question but a reference to an atom will lose the mark)
ignore discussion of SNF etc
both marks are independent
2
Page 29 of 45
(b)
✓
(i)
must see subscript and superscripts
1
(ii)
binding energy of U
= 235 × 7.59 ✓ ( = 1784 (MeV))
binding energy of Tc and In
= 112 × 8.36 + 122 × 8.51 ✓
( = 1975 (MeV))
energy released ( = 1975 – 1784) = 191 (MeV) ✓ (allow 190 MeV)
1st mark is for 235 × 7.59 seen anywhere
2nd mark for 112 × 8.36 + 122 × 8.51 or 1975 is only given if there
are no other terms or conversions added to the equation (ignore
which way round the subtraction is positioned)
correct final answer can score 3 marks
3
(iii)
energy released
= 191 × 1.60 × 10−13 ✓
( = 3.06 × 10−11 J)
loss of mass ( = E / c2 )
= 2.91 × 10−11 / (3.00 × 108)2)
= 3.4 × 10−28 (kg) ✓
or
= 191 / 931.5 u ✓ ( = 0.205 u)
= 0.205 × 1.66 × 10−27 (kg)
= 3.4 × 10−28 (kg) ✓
allow CE from (ii)
working must be shown for a CE otherwise full marks can be given
for correct answer only
note for CE
answer = (ii) × 1.78 × 10−30
(2.01 × 10−27 is a common answer)
2
(c)
(i)
line or band from origin, starting at 45° up to Z approximately = 20 reading
Z = 80, N = 110→130 ✓
initial gradient should be about 1 (ie Z = 20 ; N = 15 → 25) and
overall must show some concave curvature. (Ignore slight waviness
in the line)
if band is shown take middle as the line
if line stops at N > 70 extrapolate line to N = 80 for marking
1
Page 30 of 45
(ii)
fission fragments are (likely) to be above / to the left of the line of stability ✓
fission fragments are (likely) to have a larger N / Z ratio than stable nuclei
or
fission fragments are neutron rich owtte ✓
and become neutron or β− emitters ✓
ignore any reference to α emission
a candidate must make a choice for the first two marks
stating that there are more neutrons than protons is not enough for
a mark
1st mark reference to graph
2nd mark – high N / Z ratio or neutron rich
3rd mark beta minus
note not just beta
3
[12]
4
5
6
7
B
[1]
B
[1]
C
[1]
(a)
(i)
binding energy is the work done on nucleons to separate nucleons completely
[or the energy released by nucleons when nucleus is formed from separated
nucleons] (1)
(ii)
average
binding energy
per nucleon
curve:
correct shape, maximum at A between 40 – 60 (1)
sharp rise from <50 (binding energy)max (1)
gradual fall to > 60% (binding energy)max
scales: binding energy per nucleon to 8 – 10 MeV (1)
A to > 220 (1)
(max 5)
(b)
uranium splits into two fragments (1)
binding energy per nucleon rises (causing energy release) (1)
(2)
Page 31 of 45
(c)
number of neutrons escaping is proportional to surface area (1)
as mass increases a smaller fraction escapes (1)
because surface/volume ratio decreases (1)
hence fraction producing fission increases as mass increases (1)
(max 3)
[10]
8
(a)
(i)
proportion of U-235 is greater than in natural uranium (1)
(ii)
induced fission more probable with U-235 than with U-238 (1)
2
(b)
(i)
for steady rate of fission, one neutron per fission required to go on to produce
further fission (1)
each fission produces two or three neutrons on average (1)
some neutrons escape [or some absorbed by U-238 without fission] (1)
control rods absorb sufficient neutrons (to maintain steady rate of fission) (1)
(ii)
neutrons need to pass through a moderator (1)
to slow them (in order to cause further fissions or prevent U-238 absorbing
them) (1)
neutrons that leave the fuel rod (and pass through the moderator)
are unlikely to re-enter the same fuel rod (1)
makes it easier to replace the fuel in stages (1)
max 5
[7]
9
(a)
(i)
(ii)
three correct positions to within ±2 on x-axis (1) (1) (one mark if two correct)
(iii)
estimate of energy released:
binding energy of U-235 nucleus = (235 × 7.5) = 1763(±15)(MeV) (1)
binding energy of Sr-98 = (98 × 8.6) = 843( ± 15)(MeV) (1)
binding energy of Xe-135 = (135 × 8.4) = 1134( ± 15)(MeV) (1)
binding energy released = 1134 + 843 – 1763 = 214MeV (1)
(±40MeV)
max 6
Page 32 of 45
(b)
(i)
235g of U-235 releases 6 × 1023 × 214 × 1.6 × 10–13 J = 2.1 × 1013 (J) (1)
1.0 kg of uranium containing 3% U-235 contains 30g of U-235 (1)
energy from 1.0kg of uranium =
MeV]]
(1)
(ii)
= 2.6 × 1012 J [[1.6 × 1025
advantage:
less mass of fuel used (1) because more energy per kilogram (1)
[alternative: less harm to environment (1) because does not generate
greenhouse gases (1)
or any statement (1) argued (1)]
disadvantage:
hazardous waste (1) because fission products are radioactive (1)
[alternative: long term responsibility (1) because waste needs to be stored for
many years (1)
or any statement (1) argued (1)]
max 6
[12]
10
(a)
(i)
proton number = 36 (1)
neutron number = 56 (1)
(ii)
krypton (1)
3
(b)
one-fifth efficiency so total output (= 10 ×
= 50(MW) (1)
energy in one day = 50× 106 × 24 × 3600(J) (1) (4.32 × 1012 J)
fission atoms per day =
=1.35 ×1023 (1)
3
[6]
11
100y = 100 × 365 × 24 × 3600 (= 3.15 × 109 s) (1)
energy needed = 3.15 × 109 × 300 (1) × 10 (1) (= 9.46 × 1012 J)
number of disintegrations =
(= 2.96 × 1023) (1)
number of moles needed =
(= 0.49) (1)
molar mass = 0.239kg (1)
mass needed = 0.49 × 0.239 = 0.117 kg (1)
[7]
12
(a)
(i)
(1)
(ii)
(2)
Page 33 of 45
(b)
(Δm = mu – mBa – mKr – 4mn, electron masses balance)
Δm = 236.04573 – 144.92694 – 86.91340 – 4 × 1.00867 (1)
= 0.17071 u (1)
Q (= 0.17071 × 931.3 MeV) = 159(MeV) (1)
(3)
[5]
13
14
15
D
[1]
B
[1]
(a)
induced fission: (large) nucleus splits unto two (smaller nuclei) (1)
brought about by bombardment or collision (1)
thermal neutrons have low energies or speeds (< 1 eV) (1)
3
(b)
(i)
N = 3 (1)
(ii)
released neutrons have high(er) energies or speeds (1)
(iii)
∆m = 234.99333 - (91.90645 + 140 88354) - (2 × 1.00867) (1)
= 0.186 u (1)
(if last term in Δm omitted or incorrect number of neutrons
used in calculation, treat answer as C.E.)
energy released = 0.186 × 931 = 173 MeV (1)
(allow C.E. for ∆,m)
5
[8]
16
(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
Page 34 of 45
(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]
17
18
19
20
21
D
[1]
B
[1]
D
[1]
B
[1]
(a)
Draws appropriate triangle on graph or other mark on graph at ~ 118
B1
Change of approx 1 Me V per nucleon is multiplied by 235
B1
Multiplies by 1.6 × 10−13
B1
Quotes their answer of approx 3.8 × 10−11 to more than 2 sf
B1
4
Page 35 of 45
(b)
(2 × 2.0135) – 4.0026 seen or 0.0244 (u)
C1
Multiplies u by 1.7 × 10−27
C1
E = mc2 seen or multiplies by (3 × 108)2
C1
3.67 × 10−12J
A1
4
(c)
Multiplies 3.8 × 10−11 or their (b) by 6 × 1023
M1
attempts to convert to energy per kg by multiplying by 1000 / 4 or
1000 / 235
M1
Compares 5.5 × 1014 (J) (Hydrogen) with 9.6 × 1013 (J) (Uranium) in some
way eg by stating that the fusion reaction gives more energy (per kg) than
the fission or very similar values – must be consequent on some correct analysis
A1
3
(d)
Availability of fuel easier for fusion
B1
Doesn’t produce radioactive fission products / no waste management
problem
B1
2
[13]
22
(a)
Pa
anti (electron) neutrino
2
Page 36 of 45
(b)
2
(c)
(i)
x=4
1
(ii)
mass defect = [(232.98915 + 1.00867) –
(90.90368 + 138.87810 + 4 × 1.00867)] u
= 0.18136 u
3
energy released (= 0.18136 × 931) = 169 (MeV)
[8]
23
24
B
[1]
(a)
(i)
neutron
B1
1
(ii)
p = 36
B1
n = 144
B1
2
Page 37 of 45
(b)
(i)
total energy produced =
MJ each second
C1
number of reaction = 4.2 × 1019 per second
A1
2
(ii)
1 kg contains (1000/235) × 6.02 × 1023 atoms of uranium
C1
total number of fissions = (1000/235) × 6.02 × 1023 × 2 × 104
(5.1 × 1028)
C1
time = total fissions available/number per second or 1.2 × 109s
C1
38.7(39) years
A1
4
(iii)
too few neutrons produced to maintain the chain reaction
B1
probability of a neutron colliding with a uranium nucleus too low
B1
more absorption of neutrons in non–fission capture
B1
2
(c)
pressure = 150 × 105 (Pa) or F = PA
C1
force on 1 cm 2 = 1500N
A1
2
Page 38 of 45
(d)
energy removed each second
E=
MJ = 1.25 × 109 J or E = mc∆θ
C1
1.25 × 109 = m 5000 × 40
C1
mass per second = 6250 kg
C1
volume per second = 8.6(8.56) m3
A1
4
(e)
control rods
neutrons are absorbed
B1
by the nucleus of the boron/atoms
B1
moderator
neutrons are slowed down
B1
when colliding with the protons/hydrogen nucleus
B1
4
[21]
Page 39 of 45
Examiner reports
1
2
This question was quite discriminating overall because of its synoptic nature and other mixed
components. A majority of students got part (a) correct without too much difficulty. Those that did
not, either missed off the antineutrino or they thought this stage of the decay was initiated by a
neutron. Most students could perform the calculations required in part (b)(i). Most found the
half-life and progressed from there. A significant number of successful students substituted data
from the graph into a decay equation. Most of the students who succeeded in (b)(i) also
succeeded in (b)(ii). The most common mistake was to leave out the power of 10 from the activity
reading from the graph. Part (c)(i) caused students a number of problems. Many spent too much
time saying what a chain reaction was in very general terms without reference to the specific
situation. Many scripts started, ‘A chain reaction is when a process does something that creates
an item that is needed for another process to take place...’ Usually this was given in a much more
verbose fashion. When it did come down to the specifics students were not very careful about
using the correct terms. Although not penalised here a majority who mentioned uranium used the
238 rather than the 235 isotope. It was also common to see words like react or decay being used
where fission should have been used. Also when a single stage of the process had been written
down the next stage was not explained in sufficient detail. The words, ‘and so on’ came far too
early. In (c)(i) it was only the stronger students who knew the part played by the critical mass.
These students tended to gain both marks available for this part question because they knew
how it had an effect on the chain reaction. The majority of the other students thought the mass
had something to do with the mass of individual nuclei and its effect on an individual fission
process. The final part (c)(iii) was done poorly by all but the most able students. Most thought
that the ionisation caused by radiation made atoms radioactively unstable. Very few were aware
of the problems caused by exposure to a flux of neutrons.
(a)
The majority of candidates were able to score at least 1 mark in this explanation. Only the
best candidates were producing quality answers that gained full credit. Many candidates
were unfamiliar with the term and offered answers suggesting that these were neutrons
that were produced due to heat.
Page 40 of 45
(b)
(i)
Surprisingly, only 50% of candidates gained full marks here. A significant proportion
of candidates attempted to use the equations of motion and consequently were
awarded no marks. Candidates must be aware that these equations only apply to
situations were acceleration is constant. Some candidates lost marks by rounding the
final answer to 1 significant figure. Many lower achieving candidates failed to
correctly rearrange
mistake.
m v2 = m g h , dropping the factor of
was a common
(ii)
This was another “Show that...” style question and again it posed problems for many
candidates with just over 20% of candidates gaining 3 or 4 marks. A very large
proportion of candidates did not attempt the elastic collision part of the question and
limited themselves to 2 marks. Many of these candidates had difficulty with the vector
nature of momentum and their signs were often inconsistent or incorrect. Grade A
candidates typically presented well laid out workings that were easy-to-follow,
convincing.
(iii)
Most candidates achieved both marks here. However, some had casual use of
powers of 10 errors on their KE calculations due to keeping the mass in grams. This
of course cancelled due to the ratio aspect of the question. A number of candidates
thought that 25% was the answer; this was due to not reading the question carefully
enough.
(iv)
Most candidates gained 1 mark for stating how the demonstration related to the
moderation process. Only a small number of candidates were able to develop their
answer by providing information that was more than the converse of the information
provided, thus demonstrating a sound knowledge of the moderation process.
(v)
Just under 80% of candidates knew that water was the moderator in a PWR. A few
candidates incorrectly thought that the moderator was heavy water.
Page 41 of 45
3
In part (a) was very straightforward for many candidates. Less able candidates did not elaborate
on what the nucleus split up into or they referred to some other splitting such as fission. Another
common error was to talk about the separation of an atom into protons, neutrons and electrons.
Very few candidates got the direction of energy flow wrong.
In part (b)(i) very few candidates referred to particles other than neutrons but a significant
number failed to write down two neutrons in the correct manner.
extremely common.
and
a single were
The follow on part (b)(ii) turned out to be an extremely good discriminator. It highlighted the types
of errors candidates were making. There was a group who did not appreciate the data was given
per nucleon and used the figures without multiplying up by the respective nucleon numbers.
Another significant group added the mass energy of mostly one but sometimes two nucleons into
the proceedings. The last major group got into difficulties because they changed units
unnecessarily or only changed the units of some of the terms. Overall there was a good
percentage of correct answers.
A good proportion of candidates could accomplish the conversion of units required in part (b)(iii)
with relative ease, sometimes from an error carried forward from the previous part. With the
conversion needing two stages using the datasheet there was plenty of opportunity for errors by
dividing instead of multiplying or using an incorrect conversion factor. A separate but common
error was to ignore the answer to part (b)(ii) and simply use the difference in mass of the
nucleons involved, ignoring the binding energy per nucleon completely. Less able candidates did
not really help themselves in this question because very few put words or units to intermediate
stages of the calculation. If they had done so fewer would have lost their way.
A majority of candidates did not score marks in part (c)(i). Many knew the general shape but very
few remembered any details so they had no idea which coordinates to draw their line or band
through. Some gave no real thought to the problem and drew graphs that did not make sense.
For example some graphs went vertical or turned back on themselves.
Part (c)(ii) was very discriminating. Less able candidates simply referred to any radiation that
came to mind and forwarded very little explanation. The bulk of the candidates knew beta minus
radiation was emitted but they were not careful how they expressed their reasons. For example,
stating that there are more neutrons than protons is not sufficient to imply the nuclei are neutron
rich. A majority in this group of candidates made no reference to the graph at all. Many that did
had flawed reasoning. They thought the isotopes were neutron rich because the large number of
free neutrons in the core. Good candidates also got into some difficulty by not reading the
question carefully. Typically these candidates would start their answer with, 'If there are a lot
more neutrons than protons then... but if the neutron to proton ratio is small then…'. These
candidates obviously knew the subject matter but did not score many marks as the question
clearly asks for a choice to be made.
8
“Enrichment means giving more neutrons” was an answer for part (a)(i) given by a number of
candidates and only a minority referred to the proportion or percentage of U-235. Furthermore,
many candidates implied that U-235 changes to U-238. Quite a few superficial answers were
given in part (a)(ii) and 'more reactive' was a common sight.
Part (b)(i) was poorly answered by a majority of candidates simply because they ignored the
phrase at the beginning of the question ‘By considering the neutrons involved....’. Even good
candidates thought that fuel in a single rod would be an explosive configuration in part (b)(ii).
Page 42 of 45
9
It was not uncommon for the weaker candidates to score more than 50% of their total marks on
this question.
Parts (a)(i) and (a)(ii) were completed correctly by the vast majority of candidates and most
heeded the ‘hence’ in part (a)(iii) and attempted to use the graph, with at least partial success.
Frequently, the solution did not extend beyond using the values from the graph and treating them
as values of energy rather than energy per nucleon. A few candidates tried the more familiar
mass-defect route, which was not a viable option considering the data available in the Data
booklet.
Answers to part (b)(i), though varied in style, were often successful. Part (b)(ii) was well done,
but there were many answers of a vagueness which was not expected at Advanced level.
10
Part (a) was done well by the majority of candidates. The usual error was to confuse neutron
number with nucleon number.
Many candidates completed the calculation in part (b) successfully. The most common error was
to omit the efficiency of the power plant. It appears that candidates sometime ignore numerical
values that are given in words rather than figures. A significant number of candidates believed,
incorrectly, that 10 MW was equivalent to 1000 W.
11
12
Even weaker candidates often scored high marks in this question although, conversely, if a
question was omitted then it was usually this one. Mistakes in calculating the number of seconds
in a year were common, with much unnecessary concern about leap years and some uncertainty
about the number of weeks or days in a year. Commonly, the number of moles was calculated
correctly, although occasionally it was equated to the mass in kg, and most candidates could
then convert to the mass in g or kg. Some candidates dropped a mark for forgetting the 10%
efficiency, and those who gave no indication of their reasoning were penalised one mark,
although they often penalised themselves by losing the thread. Again, candidates who got
ridiculous answers, often by misplacing the Avogadro constant, rarely bothered to check.
The equations in part (a) were completed successfully by most candidates and there were no
recurring misconceptions. Weak candidates replaced the neutron with an alpha particle or a beta
particle, or included the wrong isotope of uranium in part (a)(i) or the wrong element in part (a)(ii).
Nearly all candidates could perform the energy calculation in part (b), with the exception of a few
weak candidates who made errors by including the mass of one neutron rather than four, or by
retaining too many significant figures in their final answer.
Page 43 of 45
15
Candidates usually had a good understanding of fission processes and most were able to make
good progress with the calculation on energy release. In a large proportion of the scripts,
candidates appreciated that induced, fission, and thermal had to be explained for the three marks
in part (a). The explanation of fission itself was not always satisfactory, because candidates
referred to atoms decaying rather than large nuclei splitting into two smaller nuclei. Almost
inevitably, a significant minority of candidates considered thermal neutrons to be ones that have
been heated up rather than ones that have been slowed down.
The calculation in part (b)(iii) produced very many fully correct solutions, even in the work of
candidates who had not been able to calculate N correctly in part (b)(i). Significant figure
penalties were, however, very common in part (iii). Because mass differences are small, it is
conventional to quote atomic masses to a large number of significant figures. Ultimately the data
in this question was limited by the three significant figures of 931 MeV, and so examiners were
not prepared to accept answers to more than four significant figures.
16
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.
21
The majority of the candidates made good progress with part (a) although, once again, their
setting out of calculations was often unconvincing. This is of particular importance in "show that"
type of questions.
Part (b) was generally well done.
A significant number of candidates failed to attempt part (c). Those that did were not happy with
the non-standard nature of the calculation.
Although candidates tended to make progress with part (d), they also tended to concentrate on
the issue of waste from fission and ignored the easy availability of fuel for fusion.
Page 44 of 45
22
The more able candidates successfully negotiated the majority of this question but the less able
found many pit-falls.
In part (a) most obtained the first mark but then did not obtain the anti-neutrino.
For part (b) some candidates did not identify the position of P. Position Q was easier for students
to identify.
A majority of candidates could balance the number of neutrons in part (c)(i) to obtain the correct
answer x = 4. Those that guessed the answer almost always gave the answer x = 3.
Part (c)(ii) was very discriminating. Less able candidates did not know how to balance the
energies and only scored marks on the conversion from u to MeV. Some did not go directly from
u to MeV and gave many lines of calculation. If correctly performed, they still got the mark for the
conversion, but they had many opportunities to show errors and so tended to be less successful
and missed the mark.
24
The neutron was identified by most students in part (a) (i).
There were many correct answers to part (a) (ii) but less able students did not take account of
the two ‘X‘ particles on the right hand side of the equation so obtained n= 145.
Most made some progress with part (b) (i). Obtaining the total energy produced by the reactor
proved difficult for less able students.
There were a good proportion of correct answers in part (b) (ii). Some progress was made by a
majority of the students.
Few were able to make a sensible comment in part (b) (iii).
Most were able to gain one of the two available marks in part (c) but the conversion from cm2 to
m2 was the downfall of many students.
Whilst many were able to gain credit in part (d) for making some progress, relatively few could
correctly complete the problem.
Most showed an appreciation of the different roles of the moderator in part (e) and the control
rods but the majority gave inadequate detail of the processes.
Page 45 of 45