Nuclear Decay Chain Calculator

Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable one, emitting radiation (alpha, beta, or gamma). The number of remaining atoms follows N(t) = N₀·e^(-λt), where λ = ln(2)/t½ is the decay constant.

A decay chain is a series of radioactive decays where the daughter product is also radioactive. For example, U-238 decays through 14 steps before reaching stable Pb-206. The Bateman equations describe the amounts of each nuclide in the chain over time.

Living organisms maintain a constant ratio of C-14/C-12 by exchanging carbon with the atmosphere. After death, C-14 decays with a half-life of 5,730 years. By measuring the remaining C-14 fraction, the age can be calculated: t = -ln(N/N₀) × t½/ln(2). Effective up to ~50,000 years.