Explain why the decay of a radioactive nucleus is described as a random and spontaneous process, and discuss how these two properties together lead to the statistical nature of radioactive decay in a large sample.

IB DP Physics Higher Level (2023 syllabus) — E.3 Radioactive decay · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

The decay of a radioactive nucleus is random because it is impossible to predict which specific nucleus will decay next or when a particular nucleus will decay. It is spontaneous because the decay occurs without any external trigger or influence – temperature, pressure, chemical state or electromagnetic fields do not affect the decay rate. Each nucleus decays independently with the same probability per unit time, characterised by the decay constant λ, so the number of decays in a given interval is proportional to the number of undecayed nuclei present. In a large sample the independent random events average out; the law of large numbers gives a smooth, predictable exponential decrease in the number of undecayed nuclei over time.

Examiner tips

  • Use the words ‘random’ and ‘spontaneous’ explicitly; link them to the impossibility of prediction and lack of external influence. Show the proportionality to λ and the number of undecayed nuclei. Mention the law of large numbers to justify the exponential trend. Keep the answer concise and structured.

Common mistakes

  • Confusing ‘random’ with ‘unpredictable’ but not stating the independence of nuclei; claiming external factors affect decay; failing to mention the decay constant λ or the proportionality to the remaining nuclei; not linking the statistical averaging to the exponential law.

Mark scheme (4 marks)

  1. Random: it is impossible to predict which specific nucleus will decay next (or when a particular nucleus will decay).
  2. Spontaneous: decay occurs without any external trigger or influence (e.g. temperature, pressure, chemical state, electromagnetic fields have no effect on the decay rate).
  3. Because each nucleus decays independently with the same probability per unit time (decay constant λ), the number of decays in a given interval is proportional to the number of undecayed nuclei present.
  4. For a large sample, the statistical behaviour of many independent random events produces a smooth, predictable exponential decay of the total number of undecayed nuclei over time (law of large numbers / statistical averaging).

Key terms in this question

random · spontaneous · statistical nature

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