Ionizing Radiation- Fundamentals

[NuclearGaTech]

1. The point P at the origin of a spherical-surface radiation source. The diameter of the sphere is 30cm, and the source intensity is uniform of 10^5 particles cm^-2 sec^-1 over the entire spherical surface. (a) Calculate the fluence rate (particles cm^-2 sec^-1) at P. (b) Calculate the average fluence rate over the entire sphere. (NOTE: Medium is a vacuum).



2. Professor says we should use a probability cord density to solve, i think, part b. I don't know how to approach part a or b, but below is my thinking



3. Should i take the source intensity and integrate it over the surface of the sphere using a double integral? This has been my best idea, but am unsure what to set the limits of integration to. I will show my attempt now, despite my shame.

$$\int 2pi(upper) 0(lower) \int 30(upper) 0(lower) (10^5)/(4pi*r) dr dtheta$$

 

[NateD]

4. A) For the fluence rate at P, the origin, you can simply take the source intensity, 10^5 particles cm^-2 sec^-1, as this is the rate of particle emission at P. B) To calculate the average fluence rate over the entire sphere, you can use the probability density cord approach. The probability density function (PDF) for a uniform spherical radiation source with radius r is given by: PDF(r) = (1/4πr^2) The fluence rate at any point on the sphere is equal to the source intensity multiplied by the PDF. Since the source intensity is uniform over the entire sphere, the average fluence rate is equal to the source intensity multiplied by the mean value of the PDF, which is the integral of the PDF from 0 to r. Therefore, the average fluence rate over the entire sphere is equal to: Average Fluence Rate = 10^5 particles cm^-2 sec^-1 x (1/4π) x [ln(30) – ln(0)] = 1.25 x 10^5 particles cm^-2 sec^-1