I performed an experiment in my physics lab course recently involving the use of a scintillator to count the number of radioactive decays that occur over a certain period. For example, I placed radioactive sodium-22 in front of the scintillators and observed a certain number of gamma decays in ten seconds.

 

In my analysis, I need to estimate the uncertainty of this measurement. Now, I know radioactive decay is a random process, so in ten seconds I may observe 107 decays, or 95, or 111. As I take larger samples over longer intervals, the random variance becomes less significant compared to the total count.

 

My question is: how do I estimate the random variance in the gamma ray count? Surely it's 97±n, where n is some number dependent on the time and decay rate, but I don't know how to calculate it.

Sampling error is [math]\sqrt{N}[/math] (assuming the noise is random)

 

97 ± 10

 

(It's why polls are always crappily reported at 3% — they sample about 1000 people, and completely ignore the large biases in their methods)

Ah, I see. And since [math]\sqrt{N}[/math] increases more slowly than [math]N[/math], the relative error decreases with the number of samples. Thanks.