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I'm working on a project, and I understand that half life of a source is typically calculated with time intervals (eg 5 sec intervals for 20 minutes) and then using that data to find the decay constant using exponential decay and then calculating the half life using ln2/decay constant, but would it be possible to calculate the half life of a source using simply one long measurement? For example if you measured a source for 20 minutes and summed up the counts of the photopeak after 20 minutes, is there anyway to get the half life from just those 2 values?

I initially thought that it seems feasible that it would be possible since it's just something like Total counts after x minutes so there has to be some relationship but if I think about it I'm actually not sure since I don't have an initial counts to use, so I can't use the exponential decay formula (at least not in the way I would expect?) and I don't have any other tools that I can think of to get the half life aside from that.

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You need at least two data points to fix the two free parameters that characterize an exponential function. So the answer is no, you would need at least one more data point to say something about the properties of that decay.

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