Question

radioactivity laboratory: question 1) If the radiation is emitted uniformly in all directions, i.e. equally over the surface of a sphere surrounding the source, what would be the value of n in equation (1)? The detector can be considered a small disk of are A on the spherical surface at a distance r. Equation (1): N = N₁r ^-n

N is intensity, n is the slope, and r is the radius. We have done a graph of Intensity vs. distance (using the log of intensity), and have calculated the slope in the laboratory. Then, we need to solve some questions, including the question above. The equation 1 is correct. I saw a Hint in a lab video that said N/N₁ = A/4 π r² Absorb A/4 π into N₁ and compare with equation 1 (that I have written above). The value of n should be 2 for the sphere. the question and the equation were copy-pasted from the laboratory manual (there is not more available information)

Answer 1

The intensity at a given distance r from the source is given to be:

N = N₁r^-n

=>

now, it is given that the radiation whose intensity is measured is emitted uniformly in all directions. This means that the radiation is emitted isotropically over the surface of sphere surrounding the source.

The surface area of a sphere is

where r is the radius of the sphere

so, if the incident power is P,

but power = intensity x area

so,

where

this means that n = 2.