Let us consider a disintegration series in which A, B, C, D, etc. are some of the intermediate consecutive atoms (i.e. between the parent element and the final stable isotope)
A stage may come when the amounts of A, B, C, D, etc. become constant, which is so because their rates of disintegration become equal. Further, if NA, NB , NC and ND, etc. represent the number of atoms of A, B, C, D, etc. at equilibrium, then
Equation 1.12 becomes
Thus, the amounts present at equilibrium are inversely proportional to their disintegration constants or directly proportional to their half-lives.
Radioactive Disintegration Series
A new element is formed when a radioactive element disintegrates and emits a or p particle. The element which emits a or p particle is called the parent element and the new element formed is called the daughter element. If the daughter element is radioactive, it again disintegrates by emitting a or p particle forming a new element. Thus, the daughter element becomes a parent element and a new daughter element is produced. This process of disintegration goes on till the end product is a stable isotope.
It may be noticed that in these series, sometimes a branched disintegration takes place (the same radioactive element can disintegrate in two different ways forming two completely different radioactive isotopes). However, both the radioactive isotopes thus formed disintegrate further to form the same radioactive isotope.