An investigation has been made to see whether the secondary X-ray photons arrive in a random manner in a commercially available X-ray fluorescence spectrometer, and if so, how may the available counting time be best used. A sufficiently large number of observations has been taken to allow a full statistical analysis to be made and compared with theoretical predictions. In addition, an experimental investigation has been made into the timing accuracy and its effect on the final count rate.
It was found that for very high counting rates, above 10 000 counts/s, or long counting times, above about 2 minutes, small instrumental errors tend to occur, but for count rates generally obtained in practice, the X-ray photons are emitted in a random manner and a Poisson distribution is obtained. In practice one could expect a single observation to be within 0.6% of the true value for a 256 000 count or 1.3% for a 64 000 count.
The necessary statistics for measurements of a given accuracy are set out in a form readily usable by the X-ray spectroscopist, together with formulae and procedure for obtaining the greatest net accuracy when only a limited time is available.