A-LevelPhysicsNuclear physics9702/41 · May/June 2020 · Q128 Marks

(a) The decay of a sample of a radioactive isotope is said to be random and spontaneous. Explain what is meant by the decay being:

(a)(i)random[1]
(a)(ii)spontaneous.[1]
(b)A radioactive isotope X has a half-life of 1.4 hours. Initially, a pure sample of this isotope X has an activity of 3.6 × 10⁵ Bq. Determine the activity of the isotope X in the sample after a time of 2.0 hours.[3]
(c)The variation with time t of the actual activity A of the sample in (b) is shown in Fig. 12.1. [Figure 12.1] (i) The initial activity of isotope X in the sample is 3.6 × 10⁵ Bq. Use information from (b) to sketch, on the axes of Fig. 12.1, the variation with time t of the activity of a pure sample of isotope X.[1]
(c)(ii)Suggest an explanation for any difference between the actual activity of the sample shown in Fig. 12.1 and the curve you have drawn for the activity of isotope X.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] time at which a nucleus will decay cannot be predicted / constant probability of decay of a nucleus
[B1] decay (of a nucleus) not affected by environmental factors
[C1] A = A₀e⁻λt and λ = ln 2 / t½
[C1] = 3.6 × 10⁵ × exp [−(2 × ln 2) / 1.4]
[C1] A = A₀ × 0.5ᴺ
[C1] = 3.6 × 10⁵ × 0.5ᴺ where N = 2/1.4
[A1] A = 1.3 × 10⁵ Bq
[B1] smooth curve, starting at (0, 3.6 × 10⁵) and passing through (1.4, 1.8 × 10⁵) and (2.0, 1.3 × 10⁵)
[C1] (activity of sample is greater than activity of X so) there must be an additional source of activity
[A1] the decay product (of isotope X) is radioactive

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