Decaya

Meet Decaya, a sample of radioactive nuclei who loses half of what is left every half-life.

An unstable nucleus can decay at any moment, and nothing about its past tells you when. Each nucleus has the same fixed chance of decaying in each second. With huge numbers of nuclei, that randomness averages out into a smooth law: after one half-life t₁/₂, half remain; after two, a quarter; after three, an eighth. In general N(t) = N₀ × 2^(−t/t₁/₂).

Example: carbon-14 has a half-life of about 5,730 years. After about 11,460 years a sample has a quarter of its original carbon-14 left. Radiocarbon dating uses this to date once-living material up to roughly 50,000 years old.

Half-lives range from tiny fractions of a second to billions of years. Uranium-238, with a half-life of about 4.5 billion years, is used to date rocks and has helped establish Earth's age.

The law describes averages. For a small number of nuclei the count fluctuates randomly, and no one can predict which nucleus will be next.