Answer to Question #1778 Submitted to "Ask the Experts"

Q

How close do analyses need to be for a parent and daughter to be considered "in equilibrium"? For example, if the concentrations of a parent and daughter as determined by chemical analysis have a 25% difference, are these "in equilibrium" or not?

A

Equilibrium between parent and daughter radionuclides usually implies either (1) that the activities of the two are essentially the same and constant over many daughter half-lives or (2) that the activities decrease at the same rate. In either case, the daughter must have a shorter half-life than the parent in order for any condition of equilibrium to be attained. If the half-life of the daughter is very much shorter, then the equilibrium is called secular. With no daughter originally present, the daughter activity reaches 99.2% of the parent activity in seven daughter half-lives. If the (shorter) daughter half-life is not greatly different from that of the parent, then the equilibrium is called transient, and the two activities decrease at the same rate. The time at which the two can be considered in transient equilibrium depends on their specific half-lives. I am not aware of any general rule used to define these states of equilibrium precisely. Equilibrium can be said to exist when the above conditions are met for all practical purposes. James E.Turner, CHP, PhD