radioactive decay

Radioactive decay is a process by which an atom of a particular isotope evolves to a different isotope by the emission of particles. See alpha decay and beta decay.

N = N₀ e^{-λ t}

Here lambda is the "decay constant", a measure of how fast the isotope decays. It is equal to (ln 2) divided by the half-life.

The equation above can be derived from the fact that since each atom of a radioactive isotope has an equal probability of decaying in a given time period, the rate of decay is proportional to the number of radioactive atoms present, i.e.:

dN/dt = -λ N.