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JEE Main 2020 (7 Jan, Shift 2) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2020 (7 Jan, Shift 2)

Q116JEE Main 2020 · 7 JAN · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

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Answer: (b)

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

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