Radioactive decay
Aggregate processes, like the radioactive decay of a lump of atoms, for which the single event probability of realization is very small but in which the number of time-slices is so large that there is nevertheless a reasonable rate of events, are modelled by the Poisson distribution, which is discrete. Radioactive decay and nuclear particle reactions are two examples of such aggregate processes. The mathematics of Poisson processes reduce to the law of exponential decay, which describes the statistical behaviour of a large number of nuclei, rather than one individual nucleus. In the following formalism, the number of nuclei or the nuclei population "N", is of course a discrete variable (a natural number)—but for any physical sample "N" is so large that it can be treated as a continuous variable. Differential calculus is used to model the behaviour of nuclear decay.