Random Errors in Radiochemistry

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Abstract
It is common practice in radiochemistry to compute precision error from the counting statistics using the Poisson distribution. We demonstrate that the empirical error in 226Ra analysis by the Lucas emanation method does not conform to this Poisson prediction. The Poisson model is inadequate because it ignores the non-Poisson error in the correction factors used to modify the counting data. We derive a theoretically more correct model and use it to investigate the error characteristics of the Lucas emanation method. Two hundred counting events and/or a counting time of 200 min will provide a precision error of between 7 and 12% (coefficient of variation) for a sample activity of 10 mBq or more and background up to 0.5 cpm. For lower activities, counting times or counting events the precision error becomes much larger. The lower limit of determination is 1.6 mBq for a counting time of 200 min, under all conditions, and it is shown that this limit is adequately predicted by the Poisson model. It is also shown that duplicate sample analysis is required to reduce the probability of gross error to an acceptable level.

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