Each unstable nucleus decays at random, but the population as a whole follows a precise exponential law set by its half-life. Alpha decay ejects a helium nucleus (2p+2n), beta decay converts a neutron to a proton by emitting an electron and antineutrino, and gamma decay releases a high-energy photon as the nucleus relaxes to a lower energy state.
N(t) = N₀ · 2^(−t / t½)
Activity A(t) = −dN/dt = (ln 2 / t½) · N(t)
- Decay mode — chooses which particle each nucleus ejects when it decays (alpha, beta, or gamma).
- Population size — number of nuclei simulated simultaneously; larger populations track the exponential curve more smoothly.
- Half-life — the time after which, on average, half the remaining nuclei have decayed.
- Time scale — speeds up or slows down the simulation clock relative to real seconds.
- Reset population — restores every nucleus to the undecayed (stable-looking) state and restarts the clock.
Real-world: this statistical decay law underlies radiocarbon dating, medical isotope dosing (e.g. iodine-131 therapy), and nuclear reactor spent-fuel handling schedules.