A-LevelPhysicsNuclear physics9702/42 · Oct/Nov 2021 · Q128 Marks
A sample of radioactive material contains atoms of an unstable nuclide X. The activity of the sample due to the atoms of X is A. The variation with time t of In A is shown in Fig. 12.1. [Figure 12.1]
- (a)(i)Radioactive decay is both random and spontaneous. State what is meant by: random[1]
- (a)(ii)State what is meant by: spontaneous.[1]
- (b)(i)Use Fig. 12.1 to determine the half-life, in minutes, of nuclide X.[3]
- (b)(ii)At time t = 0, the mass of the atoms of X in the sample is 5.66 x 10-7 kg. Determine the nucleon number of X.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- cannot predict when a particular nucleus will decay
- or cannot predict which nucleus will decay next
- (decay is) not affected by external (environmental) factors
- A = Ao exp (−λt) and so In A = In Ao – λt
- gradient of line = (−)λ
- λ = (36.4 – 35.0) / (20 – 0)
- (= 0.07(0) min-1)
- half-life = In 2 / λ
- = In 2/0.070
- = 10 min
- or Ao = exp (-36.4) = 6.43 × 1015 (Bq)
- Ao/2 = 3.21 × 1015 (Bq), so In (A0 / 2) = 35.7
- read off half-life = 10 min
- or (at one half-life,) In A = 36.4 – In 2
- = 35.7
- read off half-life = 10 min
- A = λN
- N = mass / (nucleon number × u)
- or N = (mass/nucleon number) × NA
- exp(36.4) = (1.17 × 10-3 × 5.66 × 10-7) / (nucleon number × 1.66 × 10-27)
- or exp(36.4) = (1.17 × 10-3 × 5.66 × 10–4 × 6.02 × 1023) / nucleon number
- nucleon number = 62
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