Explain why it is impossible to predict the exact moment at which a specific nucleus in a radioactive sample will decay, yet the half-life of a large sample of that nuclide can be known with great precision.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
Radioactive decay is a random process, so the decay of any individual nucleus cannot be predicted.
Each nucleus has the same constant probability of decaying per unit time (the decay constant), independent of all external factors.
When a very large number of nuclei is present, statistical averaging means the overall behaviour of the sample becomes predictable and fluctuations become negligible relative to the total.
The half‑life is therefore a well‑defined, measurable quantity for a large sample because it reflects the statistically predictable fraction of nuclei that will decay in a given time interval.
Each nucleus has the same constant probability of decaying per unit time (the decay constant), independent of all external factors.
When a very large number of nuclei is present, statistical averaging means the overall behaviour of the sample becomes predictable and fluctuations become negligible relative to the total.
The half‑life is therefore a well‑defined, measurable quantity for a large sample because it reflects the statistically predictable fraction of nuclei that will decay in a given time interval.
Examiner tips
- Use the word ‘random’ to justify unpredictability of single nuclei.
- Mention the decay constant and its independence from external factors.
- Explain statistical averaging for large numbers.
- Show that half‑life is a measurable, predictable property of the bulk sample.
Common mistakes
- Confusing the decay constant with half‑life; they are related but not the same.
- Claiming that external factors can change the decay rate.
- Over‑generalising that a single nucleus can be predicted; emphasise randomness.
Mark scheme (4 marks)
- Radioactive decay is a random process, so the decay of any individual nucleus cannot be predicted.
- Each nucleus has the same constant probability of decaying per unit time (the decay constant), independent of all external factors.
- When a very large number of nuclei is present, statistical averaging means the overall behaviour of the sample becomes predictable / fluctuations become negligible relative to the total.
- The half-life is therefore a well-defined, measurable quantity for a large sample because it reflects the statistically predictable fraction of nuclei that will decay in a given time interval.
Key terms in this question
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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