Model exponential radioactive decay with N = N₀ e^(−λt) — enter the initial amount, decay constant λ and time to get the amount remaining, or solve for λ or time. Also shows the half-life and activity.
Radioactive nuclei decay at a rate proportional to how many remain, giving exponential decay N = N₀ e^(−λt). The decay constant λ is the probability per unit time that a given nucleus decays.
λ relates directly to half-life by t½ = ln2/λ ≈ 0.693/λ. The activity (decays per second, in becquerel) is A = λN. Keep λ and t in matching time units; the calculator reports the equivalent half-life alongside the result.
N = N₀ e^(−λt): the amount remaining equals the initial amount times e to the power minus the decay constant times time.
λ is the probability per unit time that a nucleus decays. It relates to half-life by λ = ln2 / t½ and to activity by A = λN.
They are inversely related: t½ = ln2/λ ≈ 0.693/λ. A larger decay constant means a shorter half-life.
The becquerel (Bq), one decay per second. Activity A = λN falls off exponentially just like the number of nuclei.