Half-life
What is half-life?
You can't predict when one nucleus will decay, but a sample has so many that the overall pattern is predictable.
The of a radioactive isotope is:
- the time it takes for the in a sample to halve, or
- the time it takes for the (or activity) to fall to half its starting value.
Each isotope has its own half-life, from fractions of a second to billions of years.
Key terms
Finding half-life from a graph
A graph of for a radioactive source is a curve. It falls steeply at first, then more and more slowly, getting closer to zero without ever reaching it.
To find the half-life:
- Read the activity at the start.
- Halve it.
- Go across from that value to the curve, then down to the time axis.
Example: a source's activity starts at 800 Bq and the curve passes 400 Bq at 6 hours.
- Half of 800 Bq is 400 Bq, reached at 6 hours, so the half-life is 6 hours.
- After 18 hours (3 half-lives): 800 → 400 → 200 → 100 Bq.
Exam tip
Check your answer by halving again: the curve should reach 200 Bq at 12 hours.
Key terms
Net decline as a ratio (Higher tier only)
After n half-lives, the fraction of the activity left is (½)ⁿ:
| Half-lives | Fraction left |
|---|---|
| 1 | ½ |
| 2 | ¼ |
| 3 | ⅛ |
| 4 | 1/16 |
The is how much the activity has fallen: starting value − value left.
Example: a source starts at 3200 Bq. What is the net decline after 4 half-lives, as a ratio of the starting activity?
- Activity left = 3200 × 1/16 = 200 Bq
- Net decline = 3200 − 200 = 3000 Bq
- Ratio = 3000 : 3200 = 15 : 16