Setup: A radioactive source is placed at alternating distances from a Geiger Counter. Counts per second for 10 different distances (each spaced 1 cm apart) were taken for preset times ranging from 200 to 2000 seconds (depending on how far the source is from the counter).
Objective and Question: We are plotting counts per second vs source-to-counter distance for our sample, which emits beta radiation. We expect it to be $\frac{1}{r^2}$ dependance by the inverse square law, however we are getting less than $\frac{1}{r^2}$ dependance for larger distances (i.e) we are getting fewer counts than predicted by the inverse square law. At first we thought it was the air particles interacting with the beta particles, but that shouldn't have anything to do with it (according to the instructor), and the lab question hints it should have something to do with the geometry of the experiment. Can someone please help me understand this problem?
Best Answer
The reason why the inverse square law doesn't hold for a beta emitter is due to the fact that with a beta emitter we are dealing with a whole energy spectrum of beta particles (ranging from 0 eV to the maximum beta energy; in this case 2.28 MeV for 90Y). The low-energy betas are absorbed in the intermediate layer of air and the further you get from the source the more betas are absorbed by the air until you reach the maximum range in air (for the maximum beta energy 2.28 MeV of 90Y this range is 8.8 meter, for the maximum beta energy 0.546 MeV of 90Sr this range is 2 meter) and all betas are absorbed. The inverse square law for a beta emitter is valid up to approx. 30 cm in air, at greater distances the inverse square law deviates further and further.
Note: because the half-life of the daughter 90Y (64 hours) is very much shorter than that of the mother 90Sr (29 years), there is absolute equilibrium between mother and daughter, i.e. the activity of the daughter 90Y is equal to that of the mother 90Sr.