In nuclear physics, secular equilibrium is a situation in which the quantity of a radioactive isotope remains constant because its production rate (e.g., due to decay of a parent isotope) is equal to its decay rate.
Secular equilibrium can occur in a radioactive decay chain only if the half-life of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A.
The quantity of radionuclide B builds up until the number of B atoms decaying per unit time becomes equal to the number being produced per unit time.
That can be seen from the time rate of change of the number of atoms of radionuclide B: where λA and λB are the decay constants of radionuclide A and B, related to their half-lives t1/2 by
, or Over long enough times, comparable to the half-life of radionuclide A, the secular equilibrium is only approximate; NA decays away according to and the "equilibrium" quantity of radionuclide B declines in turn.