Simulation · Nuclear Physics
Radioactive Decay Simulation
This simulation plots the exponential decay curve of a radioactive sample in real time, letting you adjust the half-life and starting quantity to see how quickly different isotopes decay, with a live count of remaining nuclei and elapsed half-lives.
Interactive simulation
Elapsed time: 0.0 years
Elapsed half-lives: 0.00
Remaining: —
Percent remaining: 100.0%
The physics behind this simulation
The number of undecayed nuclei remaining after time t follows the exponential radioactive decay law:
N(t) = N₀e⁻λt, λ = ln(2)/t_½
Regardless of the half-life chosen, the shape of the curve is always the same characteristic exponential decay — only the timescale changes. After exactly one half-life, exactly 50% remains; after two, 25%; after three, 12.5%, and so on, converging toward (but never mathematically reaching) zero.
Common mistakeThis simulation shows the idealised, large-sample limit of radioactive decay. For a genuinely small number of atoms, individual decay events are discrete and random (following Poisson statistics), and the smooth exponential curve is only an accurate approximation once the sample contains a large number of atoms — which is true for virtually any macroscopic real-world sample, but not for a handful of individual atoms.
Sources
- Rutherford, E., Soddy, F. (1902). Philosophical Magazine, 4(21), 370–396.
Last verified: July 2026 · Source: Rutherford & Soddy (1902) · Confidence: high