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

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

## Mark scheme (4 marks)

1. Activity is proportional to the number of undecayed nuclei present (A = λN), so the larger sample has greater activity.
2. The decay constant λ depends only on the nature of the nucleus (the isotope), not on the size of the sample, so both samples share the same λ.
3. Half-life is related to the decay constant by t½ = ln2 / λ, so since λ is the same for both samples, the half-life is the same.
4. After one half-life each sample retains half of its original nuclei, so the larger sample still has twice as many undecayed nuclei and twice the activity as the smaller sample throughout the decay process.

## Key terms

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

## 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)
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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-two-samples-of-the-9d1cc2bc) · Published by Druglandscape Ltd.