# Explain why the activity of a radioactive sample decreases over time, even though the decay constant of the isotope remains unchanged.

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

> A freshly prepared sample of iodine-131 has an initial activity of 8.0 × 10⁵ Bq. After several weeks, the activity is measured to be significantly lower.

## Mark scheme (4 marks)

1. Activity is defined as the number of disintegrations (decays) per unit time, or A = λN.
2. Each decay event removes one undecayed nucleus from the sample, so the number of undecayed nuclei N decreases over time.
3. Since λ is constant but N decreases, the product λN (and therefore the activity) decreases over time.
4. The decrease in N (and hence activity) follows an exponential pattern, described by N = N₀e^(−λt) or A = A₀e^(−λt).

## Key terms

- [activity](https://www.gradenine.co.uk/glossary/activity)
- [decay constant](https://www.gradenine.co.uk/glossary/decay-constant)

## 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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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-activity-of-a-20b05a71) · Published by Druglandscape Ltd.