Radiological physics question

[johnq2k7]

Imagine that a point source is poisitioned at the origin of a sphere. Assume a monoenergetic isotropic photon source, emitting 10^9 photons*s^-1, each with a frequency of 2.7 x 10^20 Hz.

a.) Calculate the energy fluence rate [MeV cm^-2 s^-1] at a radial distance of 20 cm from the source. Calculate the corresponding photon fluence crossing a spherical surface elemental area (i.e a "curvy surface tile") at a radial distance of 20 cm over a time period of 10 seconds.

b.) Plot the photon fluence rate (i.e particles crossing a surface spherical elemental area per unit surface area (cm^-2) per unit time (s)) as a function of radial distance from the origin, and determine the slope of the curve. What is the common language description for this type of radiation reduction with distance?

c.) Calculate the number of photons reaching a detector subtending polar angles between 5 and 10 degrees, and azimuthal angle between 20 and 25 degrees, place at a radial distance of 5 cm, after a collection time of 1 minute.


Please help, I'm having a lot of difficulties approaching this question

 

[NateD]

. a.) The energy fluence rate at a radial distance of 20 cm from the source is given by:Energy fluence rate = (10^9 photons/s) x (2.7 x 10^20 Hz) x (3.7 x 10^-14 MeV/photon) / (4πr^2)= 1.22 x 10^-1 MeV cm^-2 s^-1The corresponding photon fluence crossing a spherical surface elemental area at a radial distance of 20 cm over a time period of 10 seconds is given by:Photon fluence = (10^9 photons/s) x (10 seconds) / (4πr^2)= 0.785 photons cm^-2b.) The photon fluence rate as a function of radial distance is given by: Photon fluence rate = (10^9 photons/s) / (4πr^2)The plot of this equation is an inverse square law, meaning that the radiation intensity decreases with the square of the distance. c.) The number of photons reaching a detector subtending polar angles between 5 and 10 degrees, and azimuthal angles between 20 and 25 degrees, placed at a radial distance of 5 cm, after a collection time of 1 minute is given by: Number of photons = (10^9 photons/s) x (60 seconds) x (ΔΩ/4π)where ΔΩ is the solid angle subtended by the detector, which is given by: ΔΩ = (10 degrees - 5 degrees)(25 degrees - 20 degrees) = 125 degrees^2 Therefore, the number of photons is given by: Number of photons = (10^9 photons/s) x (60 seconds) x (125 degrees^2/4π) = 6.37 x 10^8 photons