Physics
Radioactive decay
Watch individual nuclei decay at random while a large sample still follows a regular exponential curve.
Launch simulationHow it works
No nucleus “knows” when it will decay. Each has the same chance of decaying at every moment and has no memory: if a nucleus has survived, its chance of surviving another half-life is still 50 %. The half-life T½ is the time in which on average half of the remaining nuclei decay, so after n half-lives N₀/2ⁿ remain on average. The actual count fluctuates around the average with a standard deviation of √(N₀p(1 − p)); in a small sample the fluctuations are much larger relative to the number of nuclei.
⟨N(t)⟩ = N₀ · 2^(−t/T½)p = 2^(−t/T½)σ = √(N₀ · p · (1 − p))
Try it yourself
- With a sample of 1000 nuclei, click “Stop after one half-life”. About 500 nuclei remain, with a typical deviation of about ±16.
- Click “What survives six half-lives?”. On average 1000/64 ≈ 15.6 nuclei remain, but single trials commonly differ by ±4.
- Choose “Small sample” (50 nuclei) and press “New trial” a few times. After one half-life 25 nuclei remain on average, but the deviation of ±3.5 is much larger relative to the count than for a thousand nuclei.
- Choose “Many trials” or click “+ Add 30 trials”. Single curves fluctuate, but their average follows the theoretical exponential.
Model limitations
The model follows a single decay without daughter products, a specific isotope or a type of radiation. The 1–30 s half-life is simulated time, not a property of a real radionuclide, and the randomness comes from the browser’s pseudo-random generator. Nuclei transform; matter does not vanish.