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A photon of energy hv and momentum hv/c collides with an electron at rest. After the collision, the scattered electron and the scattered photon each make an angle of 45^{\circ} with the initial direction of motion. The ratio of frequency of scattered and incident photon is :


Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)



This is an example of Compton Scattering, which is the scattering of a photon by an electron. It results in a decrease in the energy (thus a decrease in frequency) of the photon.

Let the frequency of scattered photons be \upsilon{}'

By conservation of momentum in the vertical direction, the momentum of scattered electrons and photons are the same and equal to \frac{hv{}'}{c}

By conservation of linear momentum in the horizontal direction,

\frac{h \nu}{c}=\frac{2 h \nu^{\prime} \cos 45^{\circ}}{c} \Longrightarrow \frac{\nu^{\prime}}{\nu}=\frac{1}{\sqrt{2}}

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