Critical limit

Suppose we measure a sample that has no activity and obtain a count C in a time t. Then, we measure the background (with no sample) in the same time (count B).

We expect C~B.

The net count, S from the sample alone is the difference, S = C - B.

We repeat the pair of measurements many times (N) and plot the frequency distributions of C, B and S (see opposite).

to see the results of 100 pairs of measurements of C, B and S where the mean background count is 25. 'Continue' adds another 100 measurements.

Note how the means and standard deviations of the distributions compare.

In the limit of large N, the standard deviation of the distribution of S, s₀ = Ö(2B).

As the number of measurements increases, the distributions become better defined.