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Date	November 2020	Marks available	1	Reference code	20N.3.hl.TZ0.12
Level	HL	Paper	3	Time zone	TZ0
Command term	Outline	Question number	12	Adapted from	N/A

Question

$1.57 %$ of the mass of a rock weighing $46.5 kg$ is uranium(IV) oxide, ${UO}_{2}$ . $99.28 %$ of the uranium atoms in the rock are uranium-238, ${}^{238}U$ .

Show that the mass of the ²³⁸U isotope in the rock is $0.639 kg$ .

[2]

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.

[2]

Outline a health risk produced by exposure to radioactive decay.

[1]

Deduce the nuclear equation for the decay of uranium-238 to thorium-234.

[1]

Thorium-234 has a higher binding energy per nucleon than uranium-238. Outline what is meant by the binding energy of a nucleus.

[1]

Determine the nuclear binding energy, in $J$ , of ${}_{238}U$ using sections 2 and 4 of the data booklet.

The mass of the ${}_{238}U$ nucleus is $238.050786 amu$ .

[3]

Markscheme

$« \frac{mass %}{fraction of U in {UO}_{2}} = » \frac{238.03}{238.03 + 2 \times 16}$ / $0.881$ / $88.1 %$ ✔

$46.5 « kg » \times 0.0157 \times 0.881 \times 0.9928 « = 0.639 kg »$ ✔

Award [1 max] for omitting mass composition (giving $0.725 k g$ ).

M2 is for numerical setup, not for final value of $0.639 k g$ .

Alternative 1
$« \frac{2.23 \times 10^{10} year}{4.46 \times 10^{9} year} = » 5.00 « half - lives »$ ✔

$« m = 0.639 kg \times (0.5)^{5} = » 0.0200 « kg »$ ✔

Alternative 2
$« 𝜆 = \frac{\ln 2}{4.46 \times 10^{9} year} = » 1.554 \times 10^{- 10} « {year}^{- 1} »$ ✔

$« m = 0.639 kg \times 𝑒^{- 1.554 \times 10^{- 10 {year}^{- 1}} \times 2.23 \times 10^{10 year}} = » 0.0200 « kg »$ ✔

Award [2] for correct final answer.

Any one:

«genetic» mutations ✔

«could cause» cancer ✔
Accept specific named types of cancer.

cells «in body» altered ✔

cells «in body» cannot function ✔

damaged DNA/proteins/enzymes/organs/tissue ✔

«radiation» burns ✔

hair loss ✔

damage in foetuses ✔

damages/weakens immune system ✔

${}_{92}^{238}U \to {}_{90}^{234}{Th} + {}_{2}^{4}{He}$ ✔

Do not penalize missing atomic numbers in the equation.

Accept “ $α$ ” for " $H e$ ”.

energy required to separate a nucleus into protons and neutrons/nucleons
OR
energy released when nucleus was formed from «individual/free/isolated» protons and neutrons/nucleons ✔

Do not accept “energy released when atom was formed”.

$238.050786 « amu » \times 1.66 \times 10^{- 27} « kg {amu}^{- 1} »$
OR

✔

$(92 \times 1.672622 \times 10^{- 27}) + (146 \times 1.674927 \times 10^{- 27}) - 3.95 \times 10^{- 25}$
OR
$3.42 \times 10^{- 27} / 3 \times 10^{- 27} « kg »$ ✔

$« E = m c^{2} = 3.42 \times 10^{- 27} \times (3.00 \times 10^{8})^{2} = » 3.08 \times 10^{- 10} « J »$ ✔

Accept answers in the range “ $2.7 \times 10^{- 10} - 3.1 \times 10^{- 10} « J »$ ”.

Award [3] for correct final answer.

Examiners report

This question was generally well answered. Many candidates approached this question using amount, in mol, and converting to mass at the end. Some candidates omitted the mass composition however, resulting in a mass of 0.725 kg, which yielded [1 max].

The question involving half-life was very well answered and most scored both marks giving a final answer of 0.0200 kg, via different methods of calculation.

This question on outlining a health risk produced by exposure to radioactive decay posed no difficulty and the most common, correct answers included "could cause cancer" and "can damage DNA".

Most scored the one mark for the nuclear equation for the decay of uranium-238 to thorium-234. The most common error was including a neutron on the product side

Although many scored the one mark for outlining what is meant by the binding energy of a nucleus, the question was often answered as energy involved in the formation of an atom. Some candidates did not understand the difference between nucleus and nucleons.

This demanding question on the determination of the nuclear binding energy was well executed and many scored all three marks. Even the weaker candidates still managed to gain an ECF mark for M3 by using the E = mc² equation. The general performance on this type of calculation was much better than in previous sessions.

Syllabus sections

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

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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.
19N.3.sl.TZ0.13b:
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.
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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