[Poisson Stats] Error on half-life for radioactive decay

[henrym_]

Hi there, not sure whether this is in the right section but:

I've made two runs of a radioactive decay experiment where I've got a log(N) vs. time plots. From this I've got the decay constants and hence the half-life. I've averaged these two half-lives ( = 160 secs) and now I'm trying to work out the error associated with the half-life.

Usually I'd take the error on the fits of the two graphs and then use the error propagation equations to get the error ( = 2 secs) but I've been advised to use Poisson statistics as the error I have is likely to be an underestimate (which I agree with).

I've done some research and I've read that the standard deviation (i.e. the error) for a Poisson distribution is the square root of the mean. Does that mean I square root the two individual half-lives to get the error? (Giving me an error of approx. 16 secs)

If not, can anybody lend me help? How do I work out the final error on the half-life using Poisson statistics?

Some of the sites I've used:
https://www.colorado.edu/physics/phys2170/phys2170_fa06/downloads/poisson.pdf
https://www.phys.ufl.edu/courses/phy4803L/group_I/gamma_spec/poisson.pdf
https://ned.ipac.caltech.edu/level5/Leo/Stats2_2.html
https://www.colorado.edu/physics/phys2150/phys2150_sp14/phys2150_lec6.pdf

Thanks :)

 

[phyzguy]

Taking the square root of the half-life is not the right thing to do. You should consider in your plot of log(N) vs T that each value of N has an error of size sqrt(N), so the relative error is sqrt(N) / N = 1/sqrt(N). Then, when you do the least-squares fit of your plot of log(N) vs T you need to include the errors in the values of N. There are many descriptions on line of how to estimate the error in your slope when the points themselves have errors. At least, this is how I would approach it.