Secular Equilibrium is a condition reached when the t_phys of the parent is many times greater than the t_phys of the daughter, e.g., 100-1000 times greater or more. For example:

Ra²²⁶     ------>     Rn²²²

1620 years               3.8 days

In this case, the ratio of half-life of parent to half-life of the daughter is >155,600. To keep things in perspective, during 10 half-lives of the daughter (38 days in the example above), decay of the parent is negligible. Decay of the parent is represented by the flat line in the diagram below.

At the point at which activity of the parent and activity of the daughter become equal, equilibrium has been reached and the lines become parallel (as well as superimposed). The relationship between half-lives in secular equilibrium is

           _{apparent                   physical}

       t                        =    t

              ^{daughter                   parent}

This means that in the equilibrium mixture, the daughter appears to decay with the half-life of the parent. When the daughter is isolated from the mixture, it has its expected half-life. Perhaps the simplest explanation for their appearing to be equal is that the daughter can’t decay until it is formed, and so the rate of formation of the daughter equals the rate of decay of the parent, which is very slow. Therefore the parent and daughter appear to have the same half-lives. In the case of the decay of Ra-226 to Rn-222, the decay constant of the parent is 0.000001171day^-1 (only 1 millionth decays per day).