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  4. 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° with the initial direction of motion. The ratio of frequency of scattered and incident photon is

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Q. 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

UPSEEUPSEE 2011Dual Nature of Radiation and Matter

Solution:

$\frac{\text{Frequency of photon}}{\text{Frequency of scattered photon}}$
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$=\frac{v}{v \cos 45^{\circ}}$
$=\frac{1}{1 / \sqrt{2}}$
$=\sqrt{2}$