Some isotopes are stable (like C-12 and C-13). Others are unstable — too many or too few neutrons relative to protons makes the nucleus unstable. These are
radioactive isotopes that spontaneously emit particles or energy (radiation) as they decay toward a more stable configuration. Carbon-14 is radioactive — it decays with a half-life of about 5,730 years. Half-life is the time for half of a sample to decay. After one half-life, 50% remains. After two, 25%. After three, 12.5%. This is exponential decay — the same log mathematics as microbial death curves, just on a geological timescale.
💡 Radiocarbon dating uses C-14 half-life. By measuring how much C-14 remains in an organic sample vs how much it started with, you can calculate how long ago the organism died. The math is: t = (t₁/₂ / ln2) × ln(N₀/N) — a logarithm.