Statistics of radioactive disintegration

Whenever a physical measurement is made, it is important to know the reliability of the quantity determined. This is particularly important with radiochemical assays, for which there may be a wide variation among different measurements. The number of counts measured in a ten-minute interval may be significantly different from that obtained in another ten-minute interval—-not because of experimental error but because of statistical fluctuations. 

In this type of work we are concerned with how many events occur in a particular continuum, which in this case is a period of time. Precisely the same kind of problem arises if we are observing bacteria through a microscope, and are counting the number present in a square of a particular area the continuum with which we are then concerned is the area. 

The law which applies in problems of this kind is the Poisson distribution law, developed by the French mathematician Simeon Denis Poisson (1781-1840). According to this law, if the mean value is m counts, the probability of finding a value of x counts is 

The total probability, from 0 counts to a count of infinity, is unity  

The term in brackets is the expansion of e , and this multiplied by e is, of course, unity. The form (12.9) is very convenient, successive terms giving us the probability of obtaining 0,1, 2... counts. 

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