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

Dual Nature of Radiation and Matter

Solution:

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