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JEE Main 2021 (17 Mar, Shift 1) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2021 (17 Mar, Shift 1)

Q107JEE Main 2021 · 17 MAR · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

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)

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Answer: (b)

Electron: $p = \sqrt{2mE}$ , so $\lambda_e = \dfrac{h}{\sqrt{2mE}}$ .
Photon: $E = \dfrac{hc}{\lambda_p}$ , so $\lambda_p = \dfrac{hc}{E}$ .
$\dfrac{\lambda_e}{\lambda_p} = \dfrac{E}{c\sqrt{2mE}} = \dfrac{1}{c}\left(\dfrac{E}{2m}\right)^{1/2}$
So the answer is (b).

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