In nuclear physics
, secular equilibrium
is a situation in which the quantity of a radioactive isotope
remains constant because its production rate (due, e.g., to decay of a parent isotope) is equal to its decay rate.
Secular equilibrium in radioactive decay
<!-- Image with unknown copyright status removed: -->Secular equilibrium can only occur in a radioactive decay chain if the half-life
of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A. In such a situation, 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 timescales being 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; the quantity of radionuclide B then reaches a constant, equilibrium
value. Assuming the initial concentration of radionuclide B is zero, full equilibrium usually takes several half-lives of radionuclide B to establish.
The quantity of radionuclide B when secular equilibrium is reached is determined by the quantity of its parent A and the half-lives of the two radionuclide. This can be seen from the time rate of change of the number of atoms of radionuclide B:
- <math>frac = lambda_A N_A - lambda_B N_B</math> ,
where λ<sub>A</sub> and λ<sub>B</sub> are the decay constants
of radionuclide A and B, related to their... Read More