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.

.............................................................................................................

.............................................................................................................

(ii)     Which material is usually used for this purpose?

.............................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(3)

(b)     A fusion reaction takes place when two deuterium nuclei join, as represented by

mass of 2H nucleus      = 2.01355 u

mass of 3He nucleus    = 3.01493 umass of neutron           = 1.00867 u

Calculate

(i)      the mass difference produced when two deuterium nuclei undergo fusion,

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(ii)     the energy released, in J, when this reaction takes place.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(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,

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(ii)     state what is meant by mass difference,

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(iii)     state the relationship between binding energy and mass difference.

.............................................................................................................

.............................................................................................................(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

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(5)

(c)     Why would you expect the zinc nucleus to be very stable?

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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,

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(ii)     thermal neutrons,

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(iii)     self-sustaining chain reaction.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(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.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(ii)     Describe how the rate of fission is controlled in a nuclear reactor.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(7)

(Total 12 marks)

 

 

Q5.          (a)     The mass of a nucleus   is M.

(i)      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.

.............................................................................................................

.............................................................................................................(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.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

(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.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(5)

(Total 7 marks)

 

 

Q6.          (a)     Explain why, after a period of use, the fuel rods in a nuclear reactor become

(i)      less effective for power production,

.............................................................................................................

.............................................................................................................

.............................................................................................................

(ii)     more dangerous.

.............................................................................................................

.............................................................................................................

.............................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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  , which has adecay constant of 3.84 × 10–12 s–1.

(a)     What is meant by the decay constant?

......................................................................................................................

......................................................................................................................

......................................................................................................................

(1)

(b)     Calculate the half-life of   in years, giving your answer to an appropriate number of significant figures.

          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   atoms in this sample is 0.65 Bq.Calculate the age of the ancient boat in years.

 

 

 

 

 

 

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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(7)

(b)     Uranium is an α emitter. Explain why spent fuel rods present a greater radiation hazard than unused uranium fuel rods.

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................

......................................................................................................................(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.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(b)     State the main source of the highly radioactive waste from a nuclear reactor.

........................................................................................................................

........................................................................................................................(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.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(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.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(Total 7 marks)

Q13.(a)     (i)      Define the atomic mass unit.

...............................................................................................................

...............................................................................................................(1)

(ii)     State and explain how the mass of a   nucleus is different from the total mass of its protons and neutrons when separated.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(b)     Explain why nuclei in a star have to be at a high temperature for fusion to take place.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(3)

(c)    (i)      In massive stars, nuclei of hydrogen  are processed into nuclei of heliumthrough 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)     (i)      thickhigh densitymaterial giving minimal fatigue problems after irradiationany other sensible property e.g. withstands high temperatureany two (1) (1)

(ii)     (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 4QWC 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 3QWC 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 massof 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 4QWC 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) onefurther 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)     (i)      ∆m = Zmp + (A – Z)mn – M (1)

(ii)     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)     (i)      amount of (fissionable) uranium (235) in fuel decreases (1)fission fragments absorb neutrons (1)

(ii)     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 undergroundat 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 =  (MW) (1)(1714 MW)

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 ofA = 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 wascut 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 statisticalvariation in the recorded results

possible contamination

uncertainty in the ratio of carbon-14 in carbon thousands of years agoany 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 andnot fully coherent. There is less use of specialist vocabulary, or specialistvocabulary may be used incorrectly. The form and style of writing is lessappropriate.

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 thecritical condition.

Low Level (Poor to limited): 1 or 2 marks

The information conveyed by the answer is poorly organised and may notbe 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 tocause a further fission. Alternatively the candidate may explain one of thefollowing:the role of the moderator, the role of the control rods or can explain thecritical 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-235max 7

(b)     it is easy to stay out of range or easy to contain an α source or ß/γ havegreater 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 γradiation/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) nuclearwaste, 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 appropriately2.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 example4.Record data with more than one absorber or distances5.α source determined from results taken6.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 takenthis is a harder mark to achieveit may involve establishing an inverse square fall in intensity in air or an exponential fall using thicknesses of leadif 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 marksmarks 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 own1

(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 states2

(ii)     momentum / kinetic energy is transferred (to the moderator atoms)ora 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 independentdirection 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 / KE3

(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)orΔmass = {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 value0.02652u4.405 × 10−29 kg3.364 × 10−12 J

Δbinding energy (= 0.02652 × 931.5)      {allow 931.3}

Δbinding energy = 24.7 MeV  3rd mark – conversion to Mevconversion mark stands aloneaward 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 4Description: Shielding a reactorMarks: 7Mathematical requirements: None

Topic: Nuclear applicationsType: State/explain/describeSpecification: 5.2.2 Induced fission

N2.Question source: Legacy Spec A June 2003 Unit 4B Question 4Description: Energy release with fusionMarks: 6Mathematical requirements: Decimal and standard form | Substitution | Solve equationsTopic: Nuclear applicationsType: State/explain/numericalSpecification: 5.2.1 Mass and energy

N3.Question source: Legacy Spec A June 2004 Unit 4B Question 3Description: Binding energy; mass diff; av BE/nucleon Zinc 64Marks: 10Mathematical requirements: Substitution | Solve equationsTopic: Nuclear applicationsType: State/explain/numericalSpecification: 5.2.1 Mass and energy

N4.Question source: Legacy Spec A January 2005 Unit 4B Question 5Description: Fission terms; moderation; reaction rate controlMarks: 12Mathematical requirements: NoneTopic: Nuclear applicationsType: State/explain/describeSpecification: 5.2.2 Induced fission

N5.Question source: Legacy Spec A June 2005 Unit 4B Question 5Description: Binding energy per nucleonMarks: 7Mathematical requirements: Manipulate equations | Substitution | Translate informationTopic: Nuclear applicationsType: State/explain/numericalSpecification: 5.2.1 Mass and energy

N6.Question source: Legacy Spec A January 2006 Unit 4B Question 3Description: Fuel rods; handling and processingMarks: 8Mathematical requirements: NoneTopic: Nuclear applicationsType: State/explain/describeSpecification: 5.2.2 Induced fission | 5.2.3 Safety aspects

N7.Specification 7408Question source:Legacy Spec A June 2006 Unit 4B Question 5Description: Nuclei - fission; decrease in mass per weekMarks: 6Maths requirements: Decimal + standard form | Substitution | Solve equationsMaths demand: 2Topic: Nuclear applicationsType: Structured quantitativeSpecification: 3.8.1.6 Mass and energy

Specification 2450Question source: Legacy Spec A June 2006 Unit 4B Question 5Description: Nuclei - fission; decrease in mass per weekMarks: 6

Maths requirements: Decimal and standard form | Calculator functions | Substitution | Solve equationsTopic: Nuclear applicationsType: Structured quantitativeSpecification: 5.2.1 Mass and energy

N8.Specification 7408Question source: June 2010 Unit 5 Question 3Description: Radioactive dating of woodMarks: 11Maths requirements: Decimal + standard form | Manipulate equations | Substitution | Solve equations | Exponential + logarithmic functionsMaths demand: 2Topic: Nuclear applicationsType: Mostly numericalSpecification: 3.8.1.3 Radioactive decay

Specification 2450Question source: June 2010 Unit 5 Question 3Description: Radioactive dating of woodMarks: 11Maths requirements: Decimal and standard form | Calculator functions | Manipulate equations | Substitution | Solve equationsTopic: Nuclear applicationsType: Mostly numericalSpecification: 5.1.4 Nuclear instability

N9.Question source: June 2010 Unit 5 Question 2Description: Thermal nuclear reactorMarks: 10Mathematical requirements: NoneTopic: Nuclear applicationsType: Extended writingSpecification: 5.2.2 Induced fission | 5.2.3 Safety aspects

N10.Question source: June 2012 Unit 5 Question 3Description: Gamma ray detectorMarks: 9Mathematical requirements: Ratio; fraction; percentage | Manipulate equations | Substitution | Solve equations | Circumference; area; volumeTopic: Nuclear applicationsType: Mostly numericalSpecification: 5.1.2 alpha/beta/gamma radiation

N11.Question source: June 2013 Unit 5 Question 5Description: Describe an absorption experimentMarks: 6Mathematical requirements: Calculator functionsTopic: Nuclear applicationsType: Extended writingSpecification: 5.1.2 alpha/beta/gamma radiation

N12.Question source: June 2013 Unit 5 Question 2Description: Processes in a nuclear reactorMarks: 7Mathematical requirements: NoneTopic: Nuclear applicationsType: State/explain/describeSpecification: 5.2.2 Induced fission

N13.Question source: June 2013 Unit 5 Question 1Description: Fusion reactions in starsMarks: 12Mathematical requirements: Decimal and standard formTopic: Nuclear applicationsType: State/explain/numericalSpecification: 5.2.1 Mass and energy