In an experiment performed in the lab, I want to justify that, when the width of the Geiger counter window is approximately the same size as the distance between the window and a mildly radioactive source of Sr-90, we have a $1/r$ dependence of the counting rate. I know that we should have $1/r^2$ dependence by the inverse square law, but how do I show that, if r is relatively small, we obtain $1/r$ instead? Thank you in advance.
[Physics] 1/r Counting Rate for Radiation Experiment
data analysisexperimental-physicshomework-and-exercisesnuclear-physicsradiation
Best Answer
Look at the paths the electrons take though the active region of the counter...when the face of the counter is very near the source some of electrons will just clip the active region of the detector and may not leave enough (or any) ionization in the working gas (this is a statistical process, after all).
So the (acceptance times efficiency) goes down (various sources lump this effect into one or the other of those terms).
Not sure what the exact conditions are to get $1/r$, but how sure are you that the exponent is exactly $-1$ and not simply "weaker than $1/r^2$"?
The effect should get smaller as the detector gets increasingly far from the source, disappearing completely in the limit of range much larger than the size of the window.
This is the effect I alluded too in the last comment I made on your earlier question.