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Why are statistical considerations important in radioisotope counting?

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Why are statistical considerations important in radioisotope counting?

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While we can state that a known percentage of a radioisotope will decay over a relatively long time, within that time period we can not be certain of the instantaneous rate of decay. Thus, in any one time unit, usually in minutes, there may be x decays from a particular sample, in the next time unit there may be y, and in the next time unit z, etc. with the average over many time units being n. If we make repeated measurements, the average will always tend toward n. Therefore, the quality of a radioactivity measurement improves as the measurement is lengthened, i.e., as more data is collected. You must not be surprised if short measurements do not give precisely repeatable results; statistical treatments are available to enable the calculation of error limits, goodness of fit, etc., based upon the number of counts collected.

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