# Half-life

The time taken for half of the unstable nuclei in a sample to decay. It is also the time for the count rate to fall to half.

Physics (school) · Part 08: Atoms and radioactivity · Card 5 of 8 · Last updated 2026-10-19

## Analogy

Like a cake that halves each time you eat half of what is left: it never quite reaches zero.

## Example

**Three half-lives**

Half-life = 6 hours.
Start: 80 g
After 6 h: 40 g
After 12 h: 20 g
After 18 h: 10 g

## In practice

Doctors choose tracers with short half-lives so they vanish from the body quickly.

## Practice

### Flashcards

- **What is half-life?** The time for half the unstable nuclei in a sample to decay.

### Interview questions

**A radioactive source has a half-life of 3 hours. A sample starts with 64 g of the isotope. How much is left after 12 hours?**

- 12 hours is 4 half-lives
- Halve four times: 32, 16, 8, 4
- 4 g of the isotope remains

## Questions people ask

### How do I do a half-life calculation?

Work out how many half-lives have passed by dividing the total time by the half-life. Then halve the starting amount once for each half-life. A 80 g sample with a half-life of 6 hours leaves 80 / 2 / 2 / 2 = 10 g after 18 hours, which is three half-lives.

### Does a radioactive sample ever disappear completely?

In theory the number of unstable nuclei keeps halving and never reaches exactly zero. In practice, after many half-lives so few nuclei remain that the sample counts as safe. After ten half-lives only about one thousandth of the original sample is left.

## Related concepts

- [Radioactive decay](https://studyvisually.com/learn/science/physics-school/physics-school-part-8/physics-school-part-8-concept-3)
- [Alpha, beta and gamma](https://studyvisually.com/learn/science/physics-school/physics-school-part-8/physics-school-part-8-concept-4)
- [Ionising radiation and safety](https://studyvisually.com/learn/science/physics-school/physics-school-part-8/physics-school-part-8-concept-6)

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