Q169 / 170 · Manipal (MET) 2018 · Physics

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

  • A
    $\sqrt{E}$
  • Correct answer
    B
    $\frac{1}{\sqrt{E}}$
  • C
    $\frac{1}{E}$
  • D
    does not depend upon $E$

Solution

$\begin{aligned} & \lambda_{\text {photon }}=\frac{h c}{E} \\ & \lambda_{\text {photon }}=\frac{h}{\sqrt{2 m E}}\end{aligned}$ $\begin{aligned} \Rightarrow \quad & \frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=c \sqrt{\frac{2 m}{E}} \\ & \frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}} \propto \frac{1}{\sqrt{E}}\end{aligned}$

Hence, the correct answer is option: 'B'.

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