Zerfallsrate

Zerfallsrate, often referred to as decay rate or activity, is the rate at which a radioactive substance undergoes spontaneous decay per unit time. It describes how quickly the nuclei in a sample disappear as they transform into daughter products.

For a collection of N undecayed nuclei, the instantaneous decay rate is A = λ N, where λ is the decay constant (units of per second). The number of undecayed nuclei changes according to the differential equation dN/dt = -λ N. The activity A is thus time-dependent when N changes over time: A(t) = λ N(t).

The unit of activity in the International System is the becquerel (Bq), defined as one decay per second. The initial activity is A0 = λ N0. If the sample is large or consists of several isotopes, the total activity is the sum of the individual activities: A = Σ λi Ni.

A key relation in radioactive decay is the half-life, T1/2, the time required for the number of undecayed nuclei, and hence the activity, to fall by a factor of two. It is related to the decay constant by T1/2 = ln(2) / λ.

In practice, Zerfallsrate is used in contexts such as radiometric dating, medical imaging and therapy, nuclear safety, and detector design. Decays are random events described statistically by Poisson processes; for large numbers of nuclei, the observed decay counts follow Poisson statistics with mean proportional to the activity.