# How would you calculate the half-life of a source with one long measurement?

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.

• Yes, it is possible, see my answer. – Gert Mar 30 at 19:22
• @Gert I saw your answer and I wanted to wait for more people to just get some certainty, but I see you deleted it, I understnad why it's not completely applicable but I'd still like to see it again if possible because I did like the derivation and I'd like to mention it in my report as an assumption that I could make! thanks! – Choco-Elliot Wyvern Mar 31 at 11:22
• I've undeleted it. Ta. – Gert Mar 31 at 12:19
• You can delete it again now if you want to! I got it thank you! – Choco-Elliot Wyvern Mar 31 at 14:44