Year 11 / Ionising radiation and nuclear reactions
Random events. Predictable fractions.
The decay time of a single unstable nucleus is unpredictable. For a large sample, the expected number remaining halves in each half-life. Activity is the decay rate and follows the same exponential trend for a single isotope.
A detector also measures background. Subtract this first, then compare source count rates. Repeated counts fluctuate; longer counting intervals and repeats improve the statistical estimate.
Expected nuclei remaining
Explore the relationship
Large-sample expectation for one isotope; individual events remain random.
Remaining / %
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Time / min | Remaining / % |
|---|---|---|
| Remaining / % | 0 | 100 |
| Remaining / % | 0.333333 | 94.3874 |
| Remaining / % | 0.666667 | 89.0899 |
| Remaining / % | 1 | 84.0896 |
| Remaining / % | 1.33333 | 79.3701 |
| Remaining / % | 1.66667 | 74.9154 |
| Remaining / % | 2 | 70.7107 |
| Remaining / % | 2.33333 | 66.742 |
| Remaining / % | 2.66667 | 62.9961 |
| Remaining / % | 3 | 59.4604 |
| Remaining / % | 3.33333 | 56.1231 |
| Remaining / % | 3.66667 | 52.9732 |
| Remaining / % | 4 | 50 |
| Remaining / % | 4.33333 | 47.1937 |
| Remaining / % | 4.66667 | 44.5449 |
| Remaining / % | 5 | 42.0448 |
| Remaining / % | 5.33333 | 39.685 |
| Remaining / % | 5.66667 | 37.4577 |
| Remaining / % | 6 | 35.3553 |
| Remaining / % | 6.33333 | 33.371 |
| Remaining / % | 6.66667 | 31.498 |
| Remaining / % | 7 | 29.7302 |
| Remaining / % | 7.33333 | 28.0616 |
| Remaining / % | 7.66667 | 26.4866 |
| Remaining / % | 8 | 25 |
| Remaining / % | 8.33333 | 23.5969 |
| Remaining / % | 8.66667 | 22.2725 |
| Remaining / % | 9 | 21.0224 |
| Remaining / % | 9.33333 | 19.8425 |
| Remaining / % | 9.66667 | 18.7288 |
| Remaining / % | 10 | 17.6777 |
| Remaining / % | 10.3333 | 16.6855 |
| Remaining / % | 10.6667 | 15.749 |
| Remaining / % | 11 | 14.8651 |
| Remaining / % | 11.3333 | 14.0308 |
| Remaining / % | 11.6667 | 13.2433 |
| Remaining / % | 12 | 12.5 |
| Remaining / % | 12.3333 | 11.7984 |
| Remaining / % | 12.6667 | 11.1362 |
| Remaining / % | 13 | 10.5112 |
| Remaining / % | 13.3333 | 9.92126 |
| Remaining / % | 13.6667 | 9.36442 |
| Remaining / % | 14 | 8.83883 |
| Remaining / % | 14.3333 | 8.34275 |
| Remaining / % | 14.6667 | 7.87451 |
| Remaining / % | 15 | 7.43254 |
| Remaining / % | 15.3333 | 7.01539 |
| Remaining / % | 15.6667 | 6.62164 |
| Remaining / % | 16 | 6.25 |
| Remaining / % | 16.3333 | 5.89921 |
| Remaining / % | 16.6667 | 5.56812 |
| Remaining / % | 17 | 5.2556 |
| Remaining / % | 17.3333 | 4.96063 |
| Remaining / % | 17.6667 | 4.68221 |
| Remaining / % | 18 | 4.41942 |
| Remaining / % | 18.3333 | 4.17137 |
| Remaining / % | 18.6667 | 3.93725 |
| Remaining / % | 19 | 3.71627 |
| Remaining / % | 19.3333 | 3.50769 |
| Remaining / % | 19.6667 | 3.31082 |
| Remaining / % | 20 | 3.125 |
Explore: Increase the half-life and compare the decay curves at the same elapsed time.
A sample starts with 6400 nuclei and undergoes three half-lives.
- The remaining fraction is ()³ = .
- Expected number remaining = 800.
Assumed knowledge
Powers and graph reading.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Use half-life for nuclei and activity.
- Subtract background before analysing count rates.
READY TO TRY IT?