Question

a gieger counter placed 1 meter from a point source of radiation registers 100 counts per minute. If the geiger counter is moved closer, half-way to the source, the counting rate will be?

Answer 1

Consider that the total number of counts per minute from the point source = N
Number of counts per minute on each point at a distance of 1 m from the point source, n = N/4r²
= N/4          [Here r = 1 m]
Consider that the detector of geiger counter counter has an area of A.
Total counts per minute detected by geiger counter = nA
= NA/4
Given that NA/4 = 100

Now the distance is reduced to r = 0.5 m
Number of counts per minute on each point at a distance of 1 m from the point source, n' = N/4r²
= N/4(0.5)²
= 4N/4
Total counts per minute detected by geiger counter = n'A
= 4NA/4
= 4 x 100                 [Since NA/4 = 100]
= 400 counts per minute