Radioactive decay is the spontaneous emission of constituent particles of the nucleus of an atom, owing to its inherent instability. The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. T and P) cannot affect the rate of decay. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e.
dN/dt α N , which ends up in an equation of the type: N = Noe- λt, where No is the number of atoms of a radioactive isotope initially present and N, its number, or mass at any later instant of time, t and λ, the decay constant which is characteristic of the isotope. This equation enables us to use the observed ratio of isotopes (N/No) on two different points of time as a kind of clock that measures the time interval between two instances. This is called radiometric dating. The age of archaeological samples and minerals or even Earth can be measured by this technique. Suppose we are to determine the age of the Earth. An estimate can be obtained from arguments in nuclear physics, which says that the 235U/238U ratio may have been 1.0 when the elements formed. Thus, since N = Noe- λt we can write 235U/238U = 235Ue- λ(235)t/235Ue- λ(238)t
and solve it for t, the time. The answer is about 6 billion years. This is one fair estimate of the age of the Earth.
A number of other isotopes, viz. 14C, 232Th, 87Rb etc. are also used for the same purpose, albeit for different time-scales.