Question
Uranium-235, ${ }^{235} \mathrm{U}$, is bombarded with a neutron causing a fission reaction.
Two products of the fission of ${ }^{235} \mathrm{U}$ are ${ }^{144} \mathrm{Ba}$ and ${ }^{89} \mathrm{Kr}$.
a(i)Write the nuclear equation for this fission reaction.
a(ii) Dutline why the reaction releases energy.
b. The critical mass for weapons-grade uranium can be as small as $15 \mathrm{~kg}$. Outline what is meant by critical mass by referring to the equation in (a)(i).
c. The daughter product, ${ }^{89} \mathrm{Kr}$, has a half-life of $3.15 \mathrm{~min}$.
Calculate the time required, in minutes, for the mass of ${ }^{89} \mathrm{Kr}$ to fall to $6.25 \%$ of its initial value.
▶️Answer/Explanation
Markscheme
$$
\text { a(i) }{ }^{235} \mathrm{U}+{ }^1 \mathrm{n} \rightarrow{ }^{144} \mathrm{Ba}+{ }^{89} \mathrm{Kr}+3^1 \mathrm{n}[\boldsymbol{V}]
$$
a(iigreater binding energy per nucleon in products than reactant $[\boldsymbol{U}]$
Note: Accept “mass of products less than reactants” OR “mass converted to energy/E $=m c^2$ “.
b. mass/amount/quantity required so that «on average» each fission/reaction results in a further fission/reaction [ $\boldsymbol{V}$ ] at least one of the « 3 » neutrons produced must cause another reaction [ $]$
Note: Accept “minimum mass of fuel needed for the reaction to be self-sustaining”.
c. $« 6.25 \%=4$ half-lives, so $4 \times 3.15=» 12.6 « \min »[\boldsymbol{V}]$
Question
This question is about nuclear reactions.
Fission of a nucleus can be initiated by bombarding it with a neutron.
a(i)Determine the other product of the fission reaction of plutonium-239.
$$
{ }_{94}^{239} \mathrm{Pu}+{ }_0^1 \mathrm{n} \rightarrow{ }_{54}^{134} \mathrm{Xe}+\ldots \ldots \ldots+3{ }_0^1 \mathrm{n}
$$
a(ii)utline the concept of critical mass with respect to fission reactions.
a(iiiputline one advantage of allowing all countries access to the technology to generate electricity by nuclear fission.
b. State one advantage of using fusion reactions rather than fission to generate electrical power.
c. ${ }^{90} \mathrm{Sr}$, a common product of fission, has a half-life of 28.8 years.
Determine the number of years for the activity of a sample of ${ }^{90} \mathrm{Sr}$ to fall to one eighth $\left(\frac{1}{8}\right)$ of its initial value.
▶️Answer/Explanation
Markscheme
$$
\mathrm{a}(\mathrm{i})_{40}^{103} \mathrm{Zr}[\boldsymbol{U}]
$$
a(ii)minimum mass to «self-»sustain chain reaction
OR
if mass of fissile material is too small, too many neutrons produced pass out of the nuclear fuel
OR
at least one neutron produced causes further reaction $[\mathcal{U}]$
a(iiiAny one of:
reduction in emission of greenhouse gases «from burning fossil fuels» [ $]$
economic independence/self-sufficiency «from crude oil/producing states» $[\boldsymbol{\sim}]$
uranium is more abundant on Earth «in terms of total energy that can be produced from this fuel» than fossil fuels [ $\boldsymbol{V}$ ]
b. Any one of:
fuel is inexpensive/readily available [ $\boldsymbol{U}$ ]
no/less radioactive waste is formed $[\boldsymbol{\sim}]$
lower risk of accidents/large-scale disasters $[\boldsymbol{\sim}]$
impossible/harder to use for making materials for nuclear weapons $[\boldsymbol{\sim}]$
larger amounts of energy released per unit mass $[\boldsymbol{\sim}]$
does not require a critical mass $[\boldsymbol{V}]$
can be used continuously $[\boldsymbol{\sim}]$
Note: Accept “higher specific energy for fusion”.
Do not accept “no/less waste produced for fusion”.
Accept specific example for disasters.
c. 86.4 «years» $[\sim]$
Question
The Sun’s energy is produced by the fusion of hydrogen nuclei.
Uranium-238 produces plutonium-239, which is used as fuel in breeder reactors.
a. Explain fusion reactions with reference to binding energy.
b.i. Outline why the term breeder is used for the reactors.
b.ii.Deduce the fission reaction when ${ }^{239} \mathrm{Pu}$ is bombarded with a neutron to produce ${ }^{133} \mathrm{Xe}$ and ${ }^{103} \mathrm{Zr}$.
c. Nuclear disasters release radioactive caesium into the atmosphere, which presents serious health risks.
Cs-137 has a half-life of 30 years.
Calculate the percentage of Cs-137 remaining in the atmosphere after 240 years.
▶️Answer/Explanation
Markscheme
a. small/lighter nuclei combine to form larger/heavier nuclei
product has higher binding energy «per nucleon»
Accept binding energy curve with explanation.
b.i.converts non-fissile ${ }^{238} \mathrm{U} »$ material into fissile ${ }^{239} \mathrm{Pu}$ » material
OR
produces more fissile material than it consumes
b.ii. ${ }^{239} \mathrm{Pu}+{ }^1 \mathrm{n} \rightarrow{ }^{133} \mathrm{Xe}+{ }^{103} \mathrm{Zr}+4^1 \mathrm{n} \sim$
Accept equation with correct atomic numbers included.
Accept notation for neutrons of ” $n$ “.
Accept a correctly described equation in words.
C. ALTERNATIVE 1:
« $\frac{240}{30}=» 8 \mathrm{t}_{\frac{1}{2}} / 8$ half-lives «required»
$\%$ remaining $=« 0.50^8 \times 100=» 0.39 \ll \% »$
ALTERNATIVE 2:
$\lambda=\ll \frac{0.693}{30}=» 0.023$
$\%$ remaining $=« 100 \times \mathrm{e}^{-0.023 \times 240}=» 0.39 \ll \% »$
Award [2] for correct final answer.
Question
Nuclear fission of ${ }^{235} \mathrm{U}$ is one source of electrical energy that has a minimal carbon footprint.
a.i. Natural uranium needs to be enriched to increase the proportion of ${ }^{235} \mathrm{U}$. Suggest a technique that would determine the relative abundances of ${ }^{235} \mathrm{U}$ and ${ }^{238} \mathrm{U}$.
a.ii.Explain how ${ }^{235} \mathrm{U}$ fission results in a chain reaction, including the concept of critical mass.
b. Suggest one reason why there is opposition to the increased use of nuclear fission reactors.
Markscheme
a.i. mass spectrometry/mass spectroscopy/MS
Accept “analysis of radiation emitted”.
[1 mark]
a.ii.critical mass: mass required so that «on average» each fission/reaction results in a further fission/reaction
Any two for [2 max]:
neutron captured by « ${ }^{235} \mathrm{U}$ » nucleus
fission/reaction produces many neutrons/more than one neutron
if these cause further fission/reaction a chain reaction occurs
Nuclear fission of ${ }^{235} \mathrm{U}$ is one source of electrical energy that has a minimal carbon footprint.
a.i. Natural uranium needs to be enriched to increase the proportion of ${ }^{235} \mathrm{U}$. Suggest a technique that would determine the relative abundances of ${ }^{235} \mathrm{U}$ and ${ }^{238} \mathrm{U}$.
a.ii.Explain how ${ }^{235} \mathrm{U}$ fission results in a chain reaction, including the concept of critical mass.
b. Suggest one reason why there is opposition to the increased use of nuclear fission reactors.
▶️Answer/Explanation
Markscheme
a.i. mass spectrometry/mass spectroscopy/MS
Accept “analysis of radiation emitted”.
[1 mark]
a.ii.critical mass: mass required so that «on average» each fission/reaction results in a further fission/reaction
Any two for [2 max]:
neutron captured by « ${ }^{235} \mathrm{U}$ » nucleus
fission/reaction produces many neutrons/more than one neutron
if these cause further fission/reaction a chain reaction occurs
Accept answers in the form of suitable diagrams/equations.
[3 marks]
b. produce long lived/long half-life radioisotopes/radioactivity
OR
could be used to produce nuclear weapons
OR
«nuclear» accidents/meltdowns can occur
Accept “long lived/long half-life radioactive waste”.
[1 mark]
Question
Nuclear power is another source of energy.
a. Compare and contrast the process of nuclear fusion with nuclear fission.
b. Dubnium-261 has a half-life of 27 seconds and rutherfordium-261 has a half-life of 81 seconds.
Estimate what fraction of the dubnium-261 isotope remains in the same amount of time that $\frac{3}{4}$ of rutherfordium-261 decays.
▶️Answer/Explanation
Markscheme
a. Award [1] for one similarity:
both increase binding energy/energy yield «per nucleon»
OR
mass loss/defect in both «nuclear» reactions/mass converted to energy «from $E=m c^2$ »
OR
both produce ionizing radiation
Award [2 max] for any two differences:
in fusion, light nuclei combine to form heavier ones AND in fission, heavier nuclei split into lighter ones fission produces radioactive/nuclear waste $\boldsymbol{A N D}$ fusion does not
fission is caused by bombarding with a neutron «or by spontaneous fission» $A N D$ fusion does not
OR
fission can initiate a chain reaction $A N D$ fusion does not
fusion releases more energy per unit mass of fuel than fission
fuel is easier to obtain/cheaper for fusion reactions
fission reactions can be controlled in a power plant $A N D$ fusion cannot «yet»
fusion reactor less likely to cause a large-scale technological disaster compared to fission
fusion less dangerous than fission as radioactive isotopes produced have short half-lives so only cause a threat for a relatively short period of time fusion is in experimental development $A N D$ fission used commercially
Accept “small nuclei” OR “smaller atomic masses of nuclei” for “light nuclei” AND “large nuclei” OR “greater atomic masses of nuclei” for “heavier nuclei”.
Do not accept “no/less waste produced for fusion”.
Accept “higher specific energy for fusion”.
[3 marks]
b. $\frac{1}{64} / \frac{1}{2^6} / 0.016$
Accept “1.6\%”.
[1 mark]
Question
Landfill sites are used to dispose of about 90% of the world’s domestic waste, but incineration is being increasingly used in some countries.
Suggest why some biodegradable plastics do not decompose in landfill sites.
High-level and low-level wastes are two types of radioactive waste. Compare the half-lives and the methods of disposal of the two types of waste.
▶️Answer/Explanation
Markscheme
limited supply of oxygen (prevents the bacteria from acting);
Do not accept air.
high-level waste has longer half-life / low-level waste has shorter half-life;
high-level waste is vitrified/made into glass/buried underground/in granite/in deep mines/under water/in steel containers/in cooling ponds / OWTTE;
low-level waste is stored under water/in steel containers/in cooling ponds/filtered/discharged directly into sea / OWTTE;
Accept cooling ponds/steel containers/under water/concrete containers only once.
Examiners report
This was generally well done although few realised that oxygen was needed for the decomposition of the plastics in landfill sites.
This was generally well done although few realised that oxygen was needed for the decomposition of the plastics in landfill sites.
Question
State the characteristics and sources of low-level nuclear waste.
The disposal of nuclear waste in the sea is now banned in many countries. Discuss one method of storing high-level nuclear waste and two problems associated with it.
▶️Answer/Explanation
Markscheme
low activity and short half-life;
materials (e.g. gloves, paper towels, clothes) that have been in proximity to radioactivity / any named source (such as smoke detectors);
methods:
vitrification / encasing in concrete / burying in deep places;
problems: [2 max]
may leak into water table;
remains active for a very long time;
geological instability (e.g. earthquakes);
potential weapon for terrorists;
Examiners report
Few candidates stated both low activity and a short half-life as characteristics of low-level nuclear waste, but many correctly identified sources.
Several candidates lost a mark for the storage of high-level nuclear waste by failing to specify deep burial of the waste. The discussion of problems associated with the storage was answered reasonably well.
Question
Disposal of radioactive waste is a major ecological concern.
(a) State one source of low-level radioactive waste and one source of high-level radioactive waste.
Low-level waste:
High-level waste:
(b) Consider the following types of radioactive waste.
Identify which method can be used for the disposal of radioactive wastes A, B and C.
(i) Vitrification followed by long-term underground storage:
(ii) Storage in a non-shielded container for two months followed by the disposal as normal (non-radioactive) waste:
(iii) Ion-exchange and adsorption on iron(II) hydroxide, storage in a shielded container for 50 years, then mixing with concrete and shallow land burial:
▶️Answer/Explanation
Markscheme
(a) Low-level waste:
hospitals/radiotherapy/radiodiagnostics / food/seed/plant irradiators / smoke detectors / research laboratories / oil/coal/natural gas processing/burning/survey / uranium mill tailings / (supporting processes of) nuclear fuel cycle;
High-level waste:
(main processes of) nuclear fuel cycle / nuclear weapons / radioisotope thermoelectric generators;
Accept more specific processes/devices/etc. for both high and low level waste.
Do not accept radioactive elements/isotopes without references to their sources.
(b) (i) C;
(ii) A;
(iii) B;
Examiners report
This question was generally well answered, though on occasion candidates failed to be specific enough about the sources of nuclear waste. In the second part, many confused the preferred techniques of disposal for high level wastes with long and short half-lives.
Question
Radioactive waste must be disposed of with care.
State what is meant by the term high-level radioactive waste.
(i) Explain why high-level waste should not be disposed of by landfill or incineration.
(ii) State the name of one method of disposal used for high-level waste and explain why such a method is better than landfill and incineration.
▶️Answer/Explanation
Markscheme
highly radioactive;
(i) landfill not advisable because radioactivity can leach/escape/leak (from rain water) / OWTTE;
incineration spreads radioactivity / OWTTE;
(ii) glasification / synroc / vitrification;
locks up radioactivity for the long term;
OR
ion exchange;
concentrates radioactive material for further treatment;
OR
transmutation;
waste is turned into safer isotopes;
Examiners report
Many candidates were able to score marks in (a) and (b)(i), but in (b)(ii) they could not clearly state the name and explain why the method of disposal of high-level waste is better.
Many candidates were able to score marks in (a) and (b)(i), but in (b)(ii) they could not clearly state the name and explain why the method of disposal of high-level waste is better.
Question
Fusion and fission reactions are important nuclear reactions.
Curium, \({}^{240}{\rm{Cm}}\), was synthesized by bombarding thorium nuclei, \({}^{232}{\rm{Th}}\), with carbon-12 nuclei. State a balanced equation for this reaction.
Uranium-235 has a half-life of 7.038×108 years.
(i) Determine the time required for the mass of \({}^{235}{\rm{U}}\) in a sample originally containing 1.000 g of \({}^{235}{\rm{U}}\) to decrease to 0.125 g.
(ii) Outline why products of the fission of uranium-235 must be disposed of carefully.
Outline why an element such as thorium, Th, usually undergoes nuclear fission, whereas helium, He, undergoes nuclear fusion.
▶️Answer/Explanation
Markscheme
\[{}_{90}^{232}{\rm{Th}} + {}_6^{12}{\rm{C}} \to {}_{96}^{240}{\rm{Cm}} + 4{}_0^1{\rm{n}}\]
Accept \({}^{232}{\rm{Th}} + {}^{12}{\rm{C}} \to {}^{240}{\rm{Cm}} + 4{\rm{n}}\).
Accept ”4n” for “\(4{}_0^1{\rm{n}}\)” in any equation.
(i)
«3 half-lives, so» 2.11 × 109 «years»
Accept any value within range 2.11–2.13 × 109 «years».
(ii)
products are radioactive/undergo «nuclear» decay
OR
products have unstable nuclei
OR
products may be used to make «nuclear» weapons
both processes increase «nuclear» binding energy per nucleon
OR
both processes bring product closer to the maximum binding energy per nucleon «of iron-56»
OR
both processes result in more stable nuclei
Mark can be awarded to an annotated sketch of binding energy per nucleon vs A.
Question
Nuclear reactions transform one nuclide into another. Fission, splitting a large nucleus into two smaller nuclei, releases vast amounts of energy.
(i) Explain why fusion, combining two smaller nuclei into a larger nucleus, releases vast amounts of energy. Use section 36 of the data booklet.
(ii) Outline one advantage of fusion as a source of energy.
Radioactive phosphorus, 33P, has a half-life of 25.3 days.
(i) Calculate 33P decay constant λ and state its unit. Use section 1 of the data booklet.
(ii) Determine the fraction of the 33P sample remaining after 101.2 days.
▶️Answer/Explanation
Markscheme
i
product has higher binding energy «per nucleon»/more stable
OR
nucleons in product more tightly bound «with one another»
lighter elements «than Fe» can fuse/combine with loss of mass/mass defect «and release vast amount of energy»
Accept “mass is converted to energy” for M2
ii
Any one of:
deuterium/fuel is abundant/cheap
«helium» products not radioactive
fusion much less dangerous than fission
large amounts/shipments of radioactive fuel not required
far less radioactive waste «created by fast moving neutrons» has to be stored
Accept “reduces greenhouse gas emissions/global warming” OR “no radioactive waste” OR “more reliable power” OR “fewer safety issues”.
Do not accept “gives out a large amount of energy” as it is in the stem of the question.
i
«\(\lambda = \frac{{\ln 2}}{{{t_{\frac{1}{2}}}}} = \frac{{0.693}}{{25.3\,{\text{days}}}} = \)» 2.74 × 10−2 day−1
Need correct unit for mark.
ii
«4 half-lives; 1 →\(\frac{1}{2}\)→\(\frac{1}{4}\)→\(\frac{1}{8}\)→\(\frac{1}{16}\) =» \(\frac{1}{16}\) / 6.25 × 10−2
OR
«\(\frac{N}{{{N_0}}} = {e^{ – {\lambda _t}}} = {e^{ – 0.0274\,\, \times \,\,101.2}} = \)» 6.25 × 10−2
Accept 6.25%.
Question
Carbon is produced by fusion reactions in stars.
The main fusion reaction responsible for the production of carbon is:
X + \(_2^4{\text{He}} \to _{\;6}^{12}{\text{C}}\)
Outline how the spectra of light from stars can be used to detect the presence of carbon.
Deduce the identity of X.
Outline why this reaction results in a release of energy.
Nuclear fusion reactors are predicted to become an important source of electrical energy in the future. State two advantages of nuclear fusion over nuclear fission.
▶️Answer/Explanation
Markscheme
presence of dark/absorption lines corresponding to those found for carbon
OR
missing wavelengths/frequencies correspond to carbon’s spectrum
Accept “presence of characteristic dark lines”.
Do not accept answer in terms of emission spectra.
[1 mark]
\({}_4^8Be\)
[1 mark]
product «nucleus» has a greater binding energy «per nucleon than reacting nuclei»
Accept “mass of the products is less than mass of the reactants”.
Accept converse arguments.
[1 mark]
fuel more abundant/cheaper
no «long half-life» radioisotopes/radioactive waste
shipment of radioactive fuels not required
plutonium/nuclear weapons cannot be produced from products
nuclear disasters less likely «as no critical mass of fuel required»
higher specific energy/energy per g/kg/unit mass than fission
Do not accept simply “fusion produces more energy than fission”.
[2 marks]
Question
The sun is the main source of energy used on earth.
One fusion reaction occurring in the sun is the fusion of deuterium, \({}_1^2H\), with tritium, \({}_1^3H\), to form helium, \({}_2^4He\). State a nuclear equation for this reaction.
Explain why this fusion reaction releases energy by using section 36 of the data booklet.
State the technique used to show that the sun is mainly composed of hydrogen and helium.
Coloured molecules absorb sunlight. Identify the bonding characteristics of such molecules.
▶️Answer/Explanation
Markscheme
\({}_1^2H\) + \({}_1^3H\) → \({}_2^4He\) + \({}_0^1n\)
Accept “n” for “\({}_0^1n\)”
Accept “2H + 3H → 4He + 1n/n”.
[1 mark]
higher binding energy/BE «per nucleon» for helium/products
OR
nucleons in products more tightly bound
mass defect/lost matter converted to energy
Accept converse statement in M1.
Accept “mass deficit” for “mass defect”.
[2 marks]
spectrometry
Accept “spectroscopy” for “spectrometry” OR more specific techniques such as “atomic absorption spectrometry/AAS”, “astrophotometry” etc. Do not award mark for incorrect specific spectrometric techniques.
Do not accept “spectrum”.
[1 mark]
«extensive system of» conjugation/alternating single and double «carbon to carbon» bonds
OR
delocalized electrons «over much of the molecule»
[1 mark]
Question
In the 20th Century, both fission and fusion were considered as sources of energy but fusion was economically and technically unattainable.
Compare and contrast fission and fusion in terms of binding energy and the types of nuclei involved.
Suggest two advantages that fusion has over fission.
The amount of 228Ac in a sample decreases to one eighth \(\left( {\frac{1}{8}} \right)\) of its original value in about 18 hours due to β-decay. Estimate the half-life of 228Ac.
▶️Answer/Explanation
Markscheme
Fission: heavy nuclei AND Fusion: light nuclei
both increase in binding energy/energy yield «per nucleon»
Accept “large nuclei” OR “greater atomic masses of nuclei” for fission AND “small nuclei” OR “smaller atomic masses of nuclei” for fusion.
Award [1 max] for “Fission: heavy nuclei AND increase in binding energy «per nucleon»” OR “Fusion: light nuclei AND increase in binding energy” «per nucleon»”.
Any two of:
no/less radioactive waste produced
abundance/low cost of fuel
larger amounts of energy released per unit mass
does not require a critical mass
can be used continuously
fusion reactor less likely to cause large-scale technological disaster
Do not accept “no/less waste produced”.
Accept “higher specific energy”.
[Max 2 Marks]
6 «hours»
Question
Nuclear fission of 235U is one source of electrical energy that has a minimal carbon footprint.
Natural uranium needs to be enriched to increase the proportion of 235U. Suggest a technique that would determine the relative abundances of 235U and 238U.
Explain how 235U fission results in a chain reaction, including the concept of critical mass.
Suggest one reason why there is opposition to the increased use of nuclear fission reactors.
▶️Answer/Explanation
Markscheme
mass spectrometry/mass spectroscopy/MS
Accept “analysis of radiation emitted”.
[1 mark]
critical mass: mass required so that «on average» each fission/reaction results in a further fission/reaction
Any two for [2 max]:
neutron captured by «235U» nucleus
fission/reaction produces many neutrons/more than one neutron
if these cause further fission/reaction a chain reaction occurs
Accept “minimum mass of fuel needed for the reaction to be self-sustaining”.
Accept answers in the form of suitable diagrams/equations.
[3 marks]
produce long lived/long half-life radioisotopes/radioactivity
OR
could be used to produce nuclear weapons
OR
«nuclear» accidents/meltdowns can occur
Accept “long lived/long half-life radioactive waste”.
[1 mark]
Question
Nuclear power is another source of energy.
Compare and contrast the process of nuclear fusion with nuclear fission.
Dubnium-261 has a half-life of 27 seconds and rutherfordium-261 has a half-life of 81 seconds.
Estimate what fraction of the dubnium-261 isotope remains in the same amount of time that \(\frac{3}{4}\) of rutherfordium-261 decays.
▶️Answer/Explanation
Markscheme
Award [1] for one similarity:
both increase binding energy/energy yield «per nucleon»
OR
mass loss/defect in both «nuclear» reactions/mass converted to energy «from E = mc2»
OR
both produce ionizing radiation
Award [2 max] for any two differences:
in fusion, light nuclei combine to form heavier ones AND in fission, heavier nuclei split into lighter ones
fission produces radioactive/nuclear waste AND fusion does not
fission is caused by bombarding with a neutron «or by spontaneous fission» AND fusion does not
OR
fission can initiate a chain reaction AND fusion does not
fusion releases more energy per unit mass of fuel than fission
fuel is easier to obtain/cheaper for fusion reactions
fission reactions can be controlled in a power plant AND fusion cannot «yet»
fusion reactor less likely to cause a large-scale technological disaster compared to fission
fusion less dangerous than fission as radioactive isotopes produced have short half-lives so only cause a threat for a relatively short period of time
fusion is in experimental development AND fission used commercially
Accept “small nuclei” OR “smaller atomic masses of nuclei” for “light nuclei” AND “large nuclei” OR “greater atomic masses of nuclei” for “heavier nuclei”.
Do not accept “no/less waste produced for fusion”.
Accept “higher specific energy for fusion”.
[3 marks]
\(\frac{1}{{64}}\)/\(\frac{1}{{{2^6}}}\)/0.016
Accept “1.6%”.
[1 mark]