# 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

## 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

- [random](https://www.gradenine.co.uk/glossary/random)
- [spontaneous](https://www.gradenine.co.uk/glossary/spontaneous)
- [statistical nature](https://www.gradenine.co.uk/glossary/statistical-nature)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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