A photon and an electron have equal energy E. _ photon / _ electr… - Vidyadip

MCQ

A photon and an electron have equal energy E. $\lambda_{\text {photon }} / \lambda_{\text {electron }}$ is proportional to

A
$\sqrt{E}$
✓
$1 / \sqrt{E}$
C
$1 / E$
D
Does not depend upon $E$

✓

Answer

Correct option: B.

$1 / \sqrt{E}$

$\lambda_{\text {photon }}=\frac{h c}{E} \text { and } \lambda_{\text {proton }}=\frac{h}{\sqrt{2 m E}} $
$\Rightarrow \frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=c \sqrt{\frac{2 m}{E}} \Rightarrow \frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}} \propto \frac{1}{\sqrt{E}}$

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