Determination of the optimum counting time for finding the initial activity of a decaying source

The activity of a decaying source can be determined most accurately by choosing an optimum counting time. The choice depends on the accuracy to which the background count is known, and three possibilities are considered: (i) when the background is counted for the same time as the source; (ii) when the background is determined very accurately by counting over a long time; and (iii) when the total time for both measurements is given. Simple criteria arise when the initial count-rate from the source is either much stronger or much weaker than the background.