Open navigation menu
Physics
Radioactive decay and half-life — Random events, predictable patterns
Loading resource…
Loading resource…
Watch random nuclear decay, compare the remaining count with the theoretical curve, and explore how sample size affects fluctuations.
Hypothetical material · one dot per initial nucleus
Press Run to observe. To reach exactly T from the start, press Step ¼T four times, then compare with theory.
Remaining
100 / 100
Expected: 100
Decayed: 0
The theoretical curve shows the expected value. A finite sample can have a different count.
Half-life milestones
| Point | Simulated sample | Expected |
|---|---|---|
| 00 s | 100 | 100 |
| 1T10 s | — | 50 |
| 2T20 s | — | 25 |
| 3T30 s | — | 12.5 |
| 4T40 s | — | 6.25 |
— Not reached
Why a predictable pattern?
After each half-life, half the expected remaining population survives: 50%, 25%, 12.5%, 6.25%.
μ(t) = N₀ × 2−t/T
An expectation of 12.5 nuclei does not mean a nucleus splits in half. It is an average over many samples.
A half-life is not a countdown for an individual nucleus. A new sample follows the same law with different decay times.
Model notes
- The material is hypothetical, with a half-life of 5, 10 or 20 seconds. These are not measurements of a real isotope.
- Identical parent nuclei decay independently with a constant decay constant. Only the first decay is tracked; products are treated as stable and no chain reaction is simulated.
- Each dot represents one initial parent nucleus. Symbols, colours, sizes and positions are schematic, not representations of mass, charge, volume or visible radiation.
- The exponential curve is an expected value. A finite sample has an integer count and random fluctuations. Larger samples usually have smaller relative fluctuations, but are not always closer in every trial.
- Playback speed changes only how time is viewed. The observation ends at four half-lives for convenience; this does not imply every sample has completely decayed.
- Decay times are sampled with a reproducible pseudorandom generator for testing. This does not predict decay times of real nuclei, measure radiation dose or assess material safety.