Consequences of Violating Conditions of Counting Statistics Are Not Severe When Measuring Radon Progeny Concentrations with the Thomas and Kusnetz Methods.

When analyzing samples of radon progeny using the Thomas or Kusnetz methods, we violate one of the conditions of counting statistics because we use counting times that are not short compared with the half-lives of the radionuclides. The result is that we overestimate the uncertainties of the counts if we use counting statistics without correction. In this work, I describe the method by which I adjusted the values of variance of the counts theoretically to values that are more accurate and calculated the amounts by which I overestimate the values of counting uncertainty by using counting statistics without correction. These values are surprisingly small: 4-5% for the Thomas method and 2-3% for the Kusnetz method. Now, I can correct uncertainty values of radon progeny measurements if it is appropriate to do so. The detailed calculations I present here may be used for determining corrections to the counting uncertainty for a method for measuring radon progeny concentration using different sampling and/or counting times than those described here. Further, they may be used for any sample, not necessarily radon progeny, that requires a long counting time to acquire a significant number of observed counts.