# Explain why two samples of the same radioactive nuclide, one with twice the number of atoms as the other, will have the same half-life but different activities.

> IB DP Physics Standard Level (2023 syllabus) — E.3 Radioactive decay · Explain · 4 marks

## Mark scheme (4 marks)

1. Activity is proportional to the number of undecayed atoms present (A = λN), so the larger sample has a greater activity.
2. The decay constant λ is a fixed property of the nuclide, independent of the size of the sample.
3. Half-life is related to the decay constant by t½ = ln2 / λ, so since λ is identical for both samples, the half-life is identical.
4. After one half-life, each sample retains half its original number of atoms, so the ratio of their activities remains 2:1 throughout — both halve in the same time period.

## Key terms

- [half-life](https://www.gradenine.co.uk/glossary/half-life)

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-two-samples-of-the-993fcc6f) · Published by Druglandscape Ltd.