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%.