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Question 19N.3.sl.TZ0.13

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Date November 2019 Marks available [Maximum mark: 5] Reference code 19N.3.sl.TZ0.13
Level sl Paper 3 Time zone TZ0
Command term Calculate, Explain, State Question number 13 Adapted from N/A
13.
[Maximum mark: 5]
19N.3.sl.TZ0.13

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

(a(i))

State the nuclear equation for the fusion reaction.

[1]

Markscheme

2 4 He  +  4 8 Be → 6 12 C ✔

NOTE: Do not penalize missing atomic numbers.

(a(ii))

Explain why fusion is an exothermic process.

[2]

Markscheme

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 ✔

(b)

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

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

 

ALTERNATIVE 2
m = 4.00 ( 1 2 ) 2.01 × 10 − 16 6.70 × 10 − 17 ✔
0.500 g «of beryllium-8 remain» ✔

 

ALTERNATIVE 3
λ = «  ln ⁡ 2 6.70 × 10 − 17 »= 1.03 × 1016 «s−1» ✔
m = «  4.00   e − 1.03 × 10 16 × 2.01 × 10 − 16  =  » 0.500 «g» ✔

 

NOTE: Award [2] for correct final answer.

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