Question

For 160Co given by a MultiChannel analyser

(b) [5 marks] Calculate the energy difference between the photopeak and the Compton edge.

(c) [5 marks] Calculate the position of the backscatter peak.

Answer 1

(b) Consider the energy of the gamma ray produced from 160-Co to be .

The photopeak occurs when the amount of energy transferred, is equal the the energy of the incident gamma ray,

In a Compton scattering process, the amount of energy exchanged by the gamma ray and an electron in a material depends on the angle that the gamma ray is scattered through, and is given by the formula

where is still the energy of the incident gamma ray, is the energy of the scattered gamma ray, is the mass of the electron, is the speed of light, and is the angle that the gamma ray is scattered through.
The amount of energy exchanged is . We see that the amount of energy exchanged is maximized when , at which point the energy transferred is . We call this maximum amount of energy absorbed during Compton scattering the Compton edge.

Thus the difference is easily seen to be

The electron energy difference is similarly  . The reader can now take whichever energy they want to use.

A google search did not return the gamma spectroscopy of 160-Co (Although we do have 60-Co, with E=1.17 MeV), and so we leave the value of E to readers to look into if they have a table or if they are given the data.

(c) Given the same system, observe that the backscattering peak occurs due to the photons that leave some energy and travel exactly in angles greater than 120 degrees to that of the incidence, and hence the position is generally smeared along the graph, but by similar calculations as above, we see that it occurs at a maximum energy of .