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  • A photon and an electron (mass $m$ ) have the same energy $E$.

Q.40) A photon and an electron (mass $m$ ) have the same energy $E$. The ratio ( $\lambda_{\text {photon }} / \lambda_{\text {electron }}$ ) of their de Broglie wavelengths is: ( $c$ is the speed of light)
 

A) $\frac{1}{c} \sqrt{\mathrm{~h} / 2 m}$
 

B)  $\sqrt{E / 2 m}$
 

C)  $c \sqrt{2 m E}$
 

D) $c \sqrt{\frac{2 m}{E}}$ 

 

Answers (1)

best_answer

Q.40) Photon's wavelength:

$$
\lambda_{\text {photon }}=\frac{h c}{E}
$$


Electron's de Broglie wavelength (using non-relativistic formula):

$$
\lambda_{\text {electron }}=\frac{h}{p}=\frac{h}{\sqrt{2 m E}}
$$


Now take the ratio:

$$
\frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=\frac{h c / E}{h / \sqrt{2 m E}}=\frac{c}{E} \cdot \sqrt{2 m E}=c \cdot \sqrt{\frac{2 m}{E}}
$$

 

Posted by

Saumya Singh

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