Radioactive Half-Life

The radioactive half-life of a radioisotope is the time required for half of the atoms in a sample of that isotope to decay into another isotope. It is a property characteristic of the particular radioisotope: half-lives range from very short intervals to billions of years. It reflects nuclear stability, not the age or physical size of a particular sample. This nuclear half-life is distinct from biological or effective half-life, which concern how radioactive material is removed or reduced in a living body.

Radioactive decay is statistical: the decay time of an individual unstable nucleus cannot be predicted, but the behaviour of a large population can be described by a decay law. If N₀ is the initial number of parent nuclei, then after time t the expected number remaining is N = N₀(1/2)^(t/T₁/₂), where T₁/₂ is the half-life. Equivalently, N = N₀e^(−λt), with decay constant λ = ln(2)/T₁/₂. After one half-life, half the original nuclei remain; after two, one quarter; after three, one eighth. Decay continues rather than stopping at a particular half-life, and the remaining amount approaches zero over time.

Activity is the rate at which nuclei decay, measured in becquerels (one becquerel is one decay per second). For a given radioisotope, activity decreases along with the number of undecayed parent nuclei, following the same exponential pattern. The half-life does not specify how much material was present initially: a large and a small sample of the same isotope have the same half-life, although the larger sample has more decays per unit time while their respective numbers of parent nuclei are proportionate.

Knowing a radioisotope's half-life helps scientists estimate how its activity changes with time and select suitable isotopes for research, industrial processes and medical applications. Radiometric dating uses measured isotope abundances and known decay properties to estimate the time since a material formed or underwent a relevant exchange process. Such estimates depend on the dating method's assumptions and evidence about the sample; half-life alone does not provide an age.