Radioactive decay is a random process. Excited nuclei decay at a particular aver
ID: 1301355 • Letter: R
Question
Radioactive decay is a random process. Excited nuclei decay at a particular average rate, but it is impossible to tell when a particular excited nucleus will decay. Random processes like this are well described by "Poisson statistics". As long as the number N of counts (N must be an integer) obtained is large compared to 1 (10 is large compared to one, and even N is not too bad), a good estimate for the absolute uncertainty in N (the "standard deviation" of N) is given by rootN . This means that given a radioactive source that decays with a fixed rate (= fixed number of counts per unit time), if one repeatedly measures the number of decays for periods of time having the same duration T (this means that there is no uncertainty In T at all), the number of counts will fluctuate around some number N by an amount related to rootN. Approximately 2/3 of the results will lie in the interval between [N - root N ) and (N + root N ). The estimate for the corresponding count rate will be NIT and this rate will be governed by the same fluctuation-induced uncertainty as N. (Although N is an integer, the ratio NIT is not necessarily an integer. The statistical uncertainty in NIT is determined in the same way as for N, however, because we assume there is no uncertainty in T.) From the measured count rates we may determine the "half-lives" of radioactive nuclei. For each half-life measured, one needs to also obtain a good estimate for its uncertainty. If one has a radioactive sample and measures a count rate of NI T = 300 counts per minute, what is the estimate for the absolute uncertainty in this count rate? per minute (precise answer required with better than 0.5% accuracy). The estimate for the relative uncertainty in NIT is (as a decimal number - not a percentage - precise answer required with better than 0.5% accuracy). If you now obtain ten times as much of the same radioactive material as above, the count rate you would measure will be (about) NIT = 3,000 per minute. What is now the absolute uncertainty in the count rate? per minute (precise answer required with better than 0.5% accuracy).And what is now the relative uncertainty in NIT ? (as a decimal number -- not a percentage-- with better than 0.5 % accuracy)Explanation / Answer
a) error = sqrt(n) = sqrt(300) = 17.32
b) error/N = 17.32/300 = 0.0577
c) sqrt(3000) = 54.77
d) sqrt(3000)/3000 = 0.0183
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