Question

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 :

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

Answer 1

Answer: (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 ${\nu }^{{}^{\prime }}$

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,

$h\nu /c=2\times h{\nu }^{{}^{\prime }}cos{45}^0/c⟹{\nu }^{{}^{\prime }}/\nu =1/\sqrt{2}$

So option D is correct.