Date | November 2019 | Marks available | 2 | Reference code | 19N.3.hl.TZ0.18 |
Level | HL | Paper | 3 | Time zone | TZ0 |
Command term | Explain | 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.