| Date | November 2019 | Marks available | 3 | Reference code | 19N.3.hl.TZ0.18 |
| Level | HL | Paper | 3 | Time zone | TZ0 |
| Command term | Calculate | Question number | 18 | 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.
Explain why fusion is an exothermic process.
Calculate the heat energy released, in J, by the fusion reaction producing one atom of carbon-12. Use section 2 of the data booklet and E = mc2.
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.
Markscheme
✔
NOTE: Do not penalize missing atomic numbers.
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 ✔
Δm = «12.000000 amu − (4.002602 amu + 8.005305 amu) =» −0.007907 «amu» ✔
«0.007907 amu × 1.66 × 10−27 kg amu−1 =» 1.31 × 10−29 «kg» ✔
«E = mc2 = 1.31 × 10−29 kg × (3.00 × 108 m s−1)2 =» 1.18 × 10−12 «J» ✔
NOTE: Accept “0.007907 «amu»”.
Award [2 max] for “7.12 x 1014 «J»”.
Award [3] for correct final answer.
ALTERNATIVE 1
3 half-lives ✔
0.500 g «of beryllium-8 remain» ✔
ALTERNATIVE 2
✔
0.500 g «of beryllium-8 remain» ✔
ALTERNATIVE 3
λ = « »= 1.03 × 1016 «s−1» ✔
m = « » 0.500 «g» ✔
NOTE: Award [2] for correct final answer.
Examiners report
Syllabus sections
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17N.3.hl.TZ0.18c.i:
Calculate the loss in mass, in kg, and the energy released, in J, when 0.00100 mol of 228Ac decays, each atom losing an electron. Use section 2 of the data booklet and E = mc2.
228Ac → + 228Th
- 18N.3.hl.TZ0.12d.ii: Explain why free radicals are harmful to living cells.
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18N.3.hl.TZ0.12d.i:
Deduce a Lewis (electron dot) structure of the superoxide, O2–, free radical.
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17N.3.hl.TZ0.18c.ii:
Determine the energy released, in J, by 0.00100 mol of 228Ac over the course of 18 hours.
- 17N.3.hl.TZ0.18d: Outline how nuclear ionising radiation can damage DNA and enzymes in living cells.
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18M.3.hl.TZ2.16c.ii:
Explain, based on molecular structure and bonding, why diffusion or centrifuging can be used for enrichment of UF6 but not UO2.
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19M.3.hl.TZ2.16c:
Outline how the energy of a fission reaction can be calculated.
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18M.3.hl.TZ1.14b.ii:
Explain how the proportion of 235U in natural uranium is increased.
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17M.3.hl.TZ1.18b.ii:
The mass of X is 8.005305 amu and that of is 4.002603 amu. Determine the energy produced, in J, when one atom of is formed in this reaction. Use section 2 of the data booklet.
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19M.3.hl.TZ1.16c:
The daughter product, 89Kr, has a half-life of 3.15 min.
Calculate the time required, in minutes, for its radioactivity to fall to 10% of its initial value, using section 1 of the data booklet.
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19M.3.hl.TZ2.16d:
Calculate the half-life of an isotope whose mass falls from 5.0 × 10−5 g to 4.0 × 10−5 g in 31.4 s, using section 1 of the data booklet.
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18M.3.hl.TZ2.16c.i:
Calculate the relative rate of effusion of 235UF6(g) to 238UF6(g) using sections 1 and 6 of the data booklet.
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17M.3.hl.TZ2.16a.iii:
Calculate the energy released, in MeV, in this reaction, using section 36 of the data booklet.
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20N.3.hl.TZ0.11e(iv):
Determine the relative rate of effusion of methane () to carbon dioxide (), under the same conditions of temperature and pressure. Use section 1 of the data booklet.
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20N.3.hl.TZ0.12f:
Determine the nuclear binding energy, in , of using sections 2 and 4 of the data booklet.
The mass of the nucleus is .
-
19M.3.hl.TZ1.16a(iii):
The masses of the particles involved in this fission reaction are shown below.
Mass of neutron = 1.00867 amu
Mass of U-235 nucleus = 234.99346 amu
Mass of Ba-144 nucleus = 143.89223 amu
Mass of Kr-89 nucleus = 88.89788 amuDetermine the energy released, in J, when one uranium-235 nucleus undergoes fission. Use this data and information from sections 1 and 2 of the data booklet.
