An electron with speed v photon |MODERNPHYSICSJEEMain2022

JEE MAIN 2022

26-06-2022 S1

Question

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are $\mathrm{E}_{\mathrm{e}}$ and $\mathrm{p}_{\mathrm{e}}$ and that of photon are $\mathrm{E}_{\mathrm{ph}}$ and $\mathrm{p}_{\mathrm{ph}}$ respectively. Which of the following is correct?

Select the correct option:

$\frac{E_e}{E_{p h}}=\frac{2 c}{v}$

$\frac{E_e}{E_{p h}}=\frac{v}{2 c}$

$\frac{p_e}{p_{p h}}=\frac{2 c}{v}$

$\frac{p_e}{p_{p h}}=\frac{v}{2 c}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \lambda_e=\lambda_{\text {photon }} \\ & \frac{h}{m v}=\frac{h}{P_{\text {photon }}} \Rightarrow P_{\text {photon }}=m v \\ & \frac{E_e}{E_{p h}}=\frac{\frac{1}{2} m v^2}{\frac{h c}{\lambda}}=\frac{1}{2} \frac{m v}{P_{p h} C} \times v=\frac{v}{2 c}\end{aligned}$

Question Tags

JEE Main

Physics

Medium

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