A computer method for simulating the decay of radon daughters

The analytical equations representing the decay of a series of radioactive atoms through a number of daughter products are well known. These equations are for an idealized case in which the expectation value of the number of atoms which decay in a certain time can be represented by a smooth curve. The real curve of the total number of disintegrations from a radioactive species consists of a series of Heaviside step functions, with the steps occurring at the time of the disintegration. The disintegration of radioactive atoms is said to be random but this random behaviour is such that a single species forms an ensemble of which the times of disintegration give a geometric distribution. Numbers which have a geometric distribution can be generated by computer and can be used to simulate the decay of one or more radioactive species. A computer method is described for simulating such decay of radioactive atoms and this method is applied specifically to the decay of the short half life daughters of radon 222 and the emission of alpha particles from polonium 218 and polonium 214. Repeating the simulation of the decay a number of times provides a method for investigating the statistical uncertainty inherent in methods for measurement of exposure to radon daughters. This statistical uncertainty is difficult to investigate analytically since the time of decay of an atom of polonium 218 is not independent of the time of decay of subsequent polonium 214. The method is currently being used to investigate the statistical uncertainties of a number of commonly used methods for the counting of alpha particles from radon daughters and the calculations of exposure