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Date	November 2019	Marks available	2	Reference code	19N.3.sl.TZ0.13
Level	SL	Paper	3	Time zone	TZ0
Command term	Calculate	Question number	13	Adapted from	N/A

Question

Red supergiant stars contain carbon-12 formed by the fusion of helium-4 nuclei with beryllium-8 nuclei.

Mass of a helium-4 nucleus = 4.002602 amu
Mass of a beryllium-8 nucleus = 8.005305 amu
Mass of a carbon-12 nucleus = 12.000000 amu

State the nuclear equation for the fusion reaction.

[1]

a(i).

Explain why fusion is an exothermic process.

[2]

a(ii).

Beryllium-8 is a radioactive isotope with a half-life of 6.70 × 10⁻¹⁷ s.

Calculate the mass of beryllium-8 remaining after 2.01 × 10⁻¹⁶ s from a sample initially containing 4.00 g of beryllium-8.

[2]

Markscheme

${}_2^4{\text{He + }}{}_4^8{\text{Be}} \to {}_6^{12}{\text{C}}$ ✔

NOTE: Do not penalize missing atomic numbers.

a(i).

ALTERNATIVE 1
binding energy per nucleon is larger in carbon-12/product «than beryllium-8 and helium-4/reactants» ✔

difference in «total» binding energy is released «during fusion» ✔

ALTERNATIVE 2
mass of carbon-12/product «nucleus» is less than «the sum of» the masses of helium-4 and beryllium-8 «nuclei»/reactants
OR
two smaller nuclei form a lager nucleus ✔

mass lost/difference is converted to energy «and released»
OR
E = mc² ✔

a(ii).

ALTERNATIVE 1
3 half-lives ✔
0.500 g «of beryllium-8 remain» ✔

ALTERNATIVE 2
$m = 4.00{\left( {\frac{1}{2}} \right)^{\frac{{2.01 \times {{10}^{ - 16}}}}{{6.70 \times {{10}^{ - 17}}}}}}$ ✔
0.500 g «of beryllium-8 remain» ✔

ALTERNATIVE 3
λ = « $\frac{{\ln 2}}{{6.70 \times {{10}^{ - 17}}}}$ »= 1.03 × 10¹⁶ «s⁻¹» ✔
m = « $4.00{\text{ }}{{\text{e}}^{ - 1.03 \times {{10}^{16}} \times 2.01 \times {{10}^{ - 16}}}}{\text{ = }}$ » 0.500 «g» ✔

NOTE: Award [2] for correct final answer.

Examiners report

[N/A]

a(i).

[N/A]

a(ii).

[N/A]

Syllabus sections

Options » C: Energy » C.3 Nuclear fusion and fission

Show 52 related questions

19N.3.hl.TZ0.18a(i):
State the nuclear equation for the fusion reaction.
17M.3.sl.TZ1.14c:
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.
18M.3.sl.TZ1.12b:
Suggest one reason why there is opposition to the increased use of nuclear fission reactors.
20N.3.sl.TZ0.10b:
The half-life of ²³⁸U is $4.46 \times 10^{9}$ years. Calculate the mass of ²³⁸U that remains after $0.639 kg$ has decayed for $2.23 \times 10^{10}$ years.
18N.3.sl.TZ0.9b.i: Outline why the term breeder is used for the reactors.
18N.3.sl.TZ0.9b.ii: Deduce the fission reaction when 239Pu is bombarded with a neutron to produce 133Xe and 103Zr.
18N.3.sl.TZ0.9a: Explain fusion reactions with reference to binding energy.
18N.3.hl.TZ0.12a: Explain fusion reactions with reference to binding energy.
18N.3.hl.TZ0.12b.ii: Deduce the fission reaction when 239Pu is bombarded with a neutron to produce 133Xe and 103Zr.
18N.3.hl.TZ0.12b.i: Outline why the term breeder is used for the reactors.
19N.3.sl.TZ0.13a(ii): Explain why fusion is an exothermic process.
17N.3.sl.TZ0.14a.i:
Compare and contrast fission and fusion in terms of binding energy and the types of nuclei involved.
17M.3.sl.TZ1.14b.i:
Deduce the identity of X.
19M.3.hl.TZ1.16a(ii):
Outline why the reaction releases energy.
19M.3.sl.TZ2.11a(i):
Determine the other product of the fission reaction of plutonium-239.
18M.3.sl.TZ2.13a:
Compare and contrast the process of nuclear fusion with nuclear fission.
19M.3.sl.TZ1.12c:
The daughter product, ⁸⁹Kr, has a half-life of 3.15 min.

Calculate the time required, in minutes, for the mass of ⁸⁹Kr to fall to 6.25 % of its initial value.
19M.3.sl.TZ1.12a(ii):
Outline why the reaction releases energy.
17M.3.sl.TZ2.12a.ii:
Explain why this fusion reaction releases energy by using section 36 of the data booklet.
19M.3.sl.TZ1.12a(i):
Write the nuclear equation for this fission reaction.
19N.3.hl.TZ0.18a(ii): Explain why fusion is an exothermic process.
17N.3.sl.TZ0.14b:
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.
19M.3.sl.TZ1.12b:
The critical mass for weapons-grade uranium can be as small as 15 kg. Outline what is meant by critical mass by referring to the equation in (a)(i).
17M.3.sl.TZ1.14b.ii:
Outline why this reaction results in a release of energy.
19N.3.hl.TZ0.18b:
Beryllium-8 is a radioactive isotope with a half-life of 6.70 × 10⁻¹⁷ s.

Calculate the mass of beryllium-8 remaining after 2.01 × 10⁻¹⁶ s from a sample initially containing 4.00 g of beryllium-8.
19M.3.sl.TZ2.11a(ii):
Outline the concept of critical mass with respect to fission reactions.
16N.3.sl.TZ0.15b:
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.
19M.3.hl.TZ1.16a(i):
Write the nuclear equation for this fission reaction.
17M.3.sl.TZ1.14a:
Outline how the spectra of light from stars can be used to detect the presence of carbon.
17M.3.sl.TZ2.12a.i:
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.
19M.3.sl.TZ2.11c:
⁹⁰Sr, 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 ⁹⁰Sr to fall to one eighth ( $\frac{1}{8}$ ) of its initial value.
19M.3.hl.TZ2.16a(ii):
Outline the concept of critical mass with respect to fission reactions.
19M.3.sl.TZ2.11b:
State one advantage of using fusion reactions rather than fission to generate electrical power.
18N.3.hl.TZ0.12c:
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.
17N.3.sl.TZ0.14a.ii:
Suggest two advantages that fusion has over fission.
16N.3.sl.TZ0.15a:
(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.
19M.3.hl.TZ1.16b:
The critical mass for weapons-grade uranium can be as small as 15 kg. Outline what is meant by critical mass by referring to the equation in (a)(i).
19M.3.hl.TZ2.16a(i):
Determine the other product of the fission reaction of plutonium-239.

${}_{94}^{239}{\text{Pu + }}{}_0^1{\text{n}} \to {}_{54}^{134}{\text{Xe + }}.................{\text{ + 3}}_0^1{\text{n}}$
19M.3.hl.TZ2.16a(iii):
Outline one advantage of allowing all countries access to the technology to generate electricity by nuclear fission.
19N.3.sl.TZ0.13a(i):
State the nuclear equation for the fusion reaction.
20N.3.hl.TZ0.12d:
Deduce the nuclear equation for the decay of uranium-238 to thorium-234.
18M.3.sl.TZ2.13b:
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.
19M.3.sl.TZ2.11a(iii):
Outline one advantage of allowing all countries access to the technology to generate electricity by nuclear fission.
19M.3.hl.TZ2.16b:
State one advantage of using fusion reactions rather than fission to generate electrical power.
20N.3.hl.TZ0.12e: Thorium-234 has a higher binding energy per nucleon than uranium-238. Outline what is meant...
20N.3.sl.TZ0.10e: Thorium-234 has a higher binding energy per nucleon than uranium-238. Outline what is meant...
20N.3.sl.TZ0.10c: Outline a health risk produced by exposure to radioactive decay.
20N.3.sl.TZ0.10d:
Deduce the nuclear equation for the decay of uranium-238 to thorium-234.
18M.3.sl.TZ1.12a.ii:
Explain how ²³⁵U fission results in a chain reaction, including the concept of critical mass.
20N.3.hl.TZ0.12c: Outline a health risk produced by exposure to radioactive decay.
18N.3.sl.TZ0.9c:
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.
20N.3.hl.TZ0.12b:
The half-life of ²³⁸U is $4.46 \times 10^{9}$ years. Calculate the mass of ²³⁸U that remains after $0.639 kg$ has decayed for $2.23 \times 10^{10}$ years.

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