Question

At a distance of 10 cm from a presumably isotropic, radioactive source, a pair of students measure 55 cps (cps = counts per second). On average, how many counts per second do you expect at a distance of 22 cm?

Answer 1

With an isotropic source, you can think on the radiation like a expanding sphere, where you will measure the same cps in any point while you keep the same distance to the source, ence the radius of the sphere remains constant. So, you know that the relation depends on the radius, also, when the sphere grows, the radiation in it expands in more surface, ence the density of particles will decrease, particularly, like $\frac{1}{r^{2} }$

then, in 15cm you will have 55cps = A/(10*10) where A is the "intensity of the source" whit this you can know the value of A = 55cps*100$cm^{2}$.

then, for 22cm, Y = 55cps*100/(22*22) = 20.66 cps.