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.
In such a case, the decay rate of A and hence the production rate of B is approximately constant, because the half-life of A is very long compared to the time scales considered.
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.
, 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.