Radiometric Dating

Exponential decay and half-life in geological dating

Radioactive isotopes decay at a constant rate characterized by their half-life — the time for half the parent atoms to convert to daughter atoms. After 1 half-life, 50% remain; after 2, 25%; after 3, 12.5%. This exponential decay follows N(t) = N₀ × (1/2)^(t/t₁/₂). Different isotopes have vastly different half-lives: C-14 (5,730 years, good for organic remains up to ~50,000 years), K-40 (1.25 billion years, for ancient rocks), U-238 (4.47 billion years, for the oldest rocks and meteorites). By measuring the ratio of parent to daughter isotopes in a sample, geologists calculate its age.