Question

when looking at the intensity of radiation (like light) as a function of distance;

a) What power law should be used?

b) Why does the equation not work at close distances, but works quite well at larger ones?

c) About how far away from a Geiger counter would a Uranium-oxide glazed plate have to be in order to have the measured count rate be indistinguishable from background?

Answer 1

(a) In a case like this one we shall make use of inverse square law, which gives us a relationship between the intensity as the distance between source and observer is varied. It relates as:

(b) The inverse square applies to point sources and doesn't play well for large sources at close distances. But at large distances even large sources will act and appear like a point source thus making the law viable and useful. But at close distances the size of source is not very small as compared to the distance between source and observer. Thus we need large distances for the equation to work well.

(c) The maximum distance at which we can put the source so that it can be distinguished from the background counts can be found by using the inverse square law itself. Let us assume the background counts to have an intensity of I_b then in order to be distinguishable this value should be lower than I, thus pluggin this relationship in the formula above we get:

and

Using this inequality we can assume the maximum distance.