An electron of mass $m$ and a photon have same

Question:

An electron of mass $m$ and a photon have same

energy E. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)

  1. (1) $\frac{1}{c}\left(\frac{2 m}{E}\right)^{1 / 2}$

  2. (2) $\frac{1}{c}\left(\frac{E}{2 m}\right)^{1 / 2}$

  3. (3) $\left(\frac{E}{2 m}\right)^{1 / 2}$

  4. (4) $\mathrm{c}(2 \mathrm{mE})^{1 / 2}$


Correct Option: , 2

Solution:

(2)

$\lambda_{1}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$

$\lambda_{2}=\frac{\mathrm{hc}}{\mathrm{E}}$

$\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{c}\left(\frac{\mathrm{E}}{2 \mathrm{~m}}\right)^{1 / 2}$

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