Question

A photon of energy $h\nu$ and momentum $h\nu /c$ 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 :
(correct answer + 1, wrong answer - 0.25)

• A. $\sqrt{2}$
• B. $\sqrt{2}-1$
• C. $2$
• D. $1/\sqrt{2}$

Answer 1

The correct option is D $1/\sqrt{2}$

This is an example of Compton Scattering, which is scattering of a photon by an electron. It results in a decrease in energy (thus decrease in frequency) of the photon.
Let the frequency of scattered photon be $v$
By conservation of momentum in vertical direction, the momentum of scattered electron and photon are same and equal to $h{\nu }^{\prime }/c$ .
By conservation of linear momentum in horizontal direction,
$h\nu /c=2\times h{\nu }^{\prime }\cos {45}^{\circ }/\text{C}\Rightarrow {\nu }^{\prime }/\nu =1/\sqrt{2}$
So option (d) is correct.