# Explain why a graph of the number of undecayed nuclei N against time t for a radioactive sample produces an exponential curve, and explain what feature of the curve allows the half-life to be determined without knowing the initial number of nuclei.

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

## Mark scheme (4 marks)

1. The rate of decay (activity) is proportional to the number of undecayed nuclei present at that instant.
2. This proportionality means the fractional rate of change of N is constant (equal to the decay constant λ), which is the defining condition for exponential decay.
3. The half-life is the time interval for N to halve from any chosen value on the curve, not just from the start.
4. This constancy of the half-life (a property of exponential functions) means N₀ need not be known; the same time interval for halving is read directly from the graph at any convenient point.

## Key terms

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

## 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-a-graph-of-the-ae555c23) · Published by Druglandscape Ltd.