- #1

xago

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## Homework Statement

Consider the situation where high-energy gamma rays are striking a detector after

scattering off of the electrons in the material surrounding a detector. Show that if

the gamma rays are perfectly back-scattered by the material, such that the scattering

angle is θ = 180 degrees, then the detected scattered photons will all have essentially

the same energy of 0.26 MeV, independent of the precise energy of the incident gamma

rays as long as the incident gamma ray energy is much larger than the rest-mass energy

of an electron.

## Homework Equations

[tex]\lambda[/tex]

_{final}- [tex]\lambda[/tex]

_{initial}= [tex]\frac{h}{(me)c}[/tex] (1 - cos[tex]\theta[/tex])

## The Attempt at a Solution

Well for [tex]\theta[/tex] = 180 degrees, the compton scattering eqn becomes

[tex]\lambda[/tex]

_{final}- [tex]\lambda[/tex]

_{initial}= [tex]\frac{2h}{(me)c}[/tex].

I'm confused about where to go from here since [tex]\lambda[/tex]

_{final}- [tex]\lambda[/tex]

_{initial}needs to be proven it is 0, and also that [tex]\lambda[/tex]

_{final}= [tex]\lambda[/tex]

_{initial}= 0.26MeV.

I have a feeling I need to to use the binomial expansion somewhere since it is saying that the incident gamma ray energy has to be much larger than the rest-mass energy

of an electron. Can someone push me in the right direction?