Compute radioactive decay or find the half-life given initial and final quantities.
Half-life (t½) is the time required for a quantity to reduce to half its initial value. It is commonly used in nuclear physics to describe radioactive decay, but also applies to chemical reactions and pharmacokinetics.
N(t) = N₀ × (1/2)^(t / t½). The decay constant λ = ln(2) / t½, and the time constant τ = 1/λ = t½ / ln(2).
Given initial N₀, final N, and elapsed time t, the half-life is t½ = t / log₂(N₀/N). Rearranged: t½ = t × ln(2) / ln(N₀/N).
The decay constant λ = ln(2) / t½ represents the probability of decay per unit time. It is related to the half-life: a shorter half-life means a larger decay constant and faster decay.