A-LevelPhysicsNuclear physics9702/41 · Oct/Nov 2018 · Q1211 Marks

The variation with time t of the number N of undecayed nuclei in a sample of a radioactive isotope is shown in [Figure 12.1].

(a)State what is meant by radioactive decay.[3]
(b)(i)Use the gradient of the line in [Figure 12.1] to determine the activity, in Bq, of the sample at time t = 4.0 hours. Show your working. activity = ........................................................... Bq[3]
(b)(ii)Use your answer in (i) to show that the decay constant λ of the isotope is approximately 4 × 10⁻⁵ s⁻¹.[2]
(c)A sample of a different radioactive isotope has an initial activity of 4.6 × 10³ Bq. The sample must be stored safely until its activity is reduced to 1.0 × 10³ Bq. The decay constant of the isotope is 5.5 × 10⁻⁷ s⁻¹. The decay products are not radioactive. Calculate the minimum time, in days, for which the sample must be stored. time = ........................................................... days[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] unstable nucleus
[B1] emission of particles/photons
[B1] emission is spontaneous or (particles/radiation) are ionising
[B1] tangent drawn and gradient calculation attempted
[A2] activity = 1.3 × 10⁶ Bq (1 mark for answer within ±0.2 × 10⁶ Bq, 2 marks for answer within ±0.1 × 10⁶ Bq)
[C1] A = λN
[A1] λ = (1.3 × 10⁶)/(3.05 × 10¹⁰) = 4.3 × 10⁻⁵ s⁻¹ (≈ 4 × 10⁻⁵ s⁻¹)
[C1] A = A₀e⁻λt
[C1] 1.0 × 10³ = 4.6 × 10³ exp(–5.5 × 10⁻⁷ × t) or ln (4.6) = 5.5 × 10⁻⁷ x t
[A1] t = 2.78 x 10⁶ s = 32 days

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