# A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.

A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.
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autosmut6p
For the photon:
${E}_{1}=\frac{hc}{{\lambda }_{1}}\phantom{\rule{0ex}{0ex}}⇒{\lambda }_{1}=\frac{hc}{{E}_{1}}$
Substitute for for c, and for h

By using the Compton's effect:
${\lambda }_{2}-{\lambda }_{1}=\frac{h}{{m}_{p}c}\left(1-\mathrm{cos}\theta \right)$
Here, the maximum possible change of energy takes place when the photon recoils in the opposite direction to that of the incident direction.
When $\mathrm{cos}\theta =-1$ therefore,
$\theta ={\mathrm{cos}}^{-1}\left(-1\right)\phantom{\rule{0ex}{0ex}}\theta ={180}^{\circ }$
Substitute for for for for c, and for h into equation.

The lose of energy is,
$\mathrm{△}E={E}_{2}-{E}_{1}\phantom{\rule{0ex}{0ex}}=\frac{hc}{{\lambda }_{2}}-\frac{hc}{{\lambda }_{1}}$
So:

Hence, the maximum energy loss that the photon can suffer is