Simple methods for calculating activity of a parent-progeny system

Based on the original work of Rutherford (Radio-activity, 1905) and Bateman (Proc Camb Philos Soc 15:423–427, 1910), the authors designed two schemes consisting of explicit equations as simple methods for accurately obtaining activity of 90Sr and 90Y before they reach secular equilibrium. Application of the methods to the 90Sr/90Y system where 90Sr and 90Y are not in equilibrium will substantially reduce the time needed for determining activity of 90Sr because neither sequential measurements of 90Sr or 90Y (up to about 2 weeks) nor waiting for 90Sr and 90Y to reach equilibrium (more than 3 weeks) will be needed. We also implemented the explicit equations for decay/ingrowth correction of progeny’s activity and applied them to the 95Zr/95Nb system. Using the equations, the authors corrected activity concentrations of 95Nb to a designated reference time from the activity concentrations measured from samples at different times, for instance, 2, 8, 15, and 29 days after a reference time. During those measurement times, 95Nb and 95Zr were not in equilibrium. The corrected 95Nb activity concentrations were within an accuracy of − 10%.