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JEE Main 2024 (29 Jan, Shift 1) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2024 (29 Jan, Shift 1)

Q60JEE Main 2024 · 29 JAN · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $25\%$ of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

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Answer: (c)

Same $\lambda$ means same momentum $p = mv$ .
Electron: $K_e = \frac{1}{2}mv^2 = \frac{1}{2}pv$ . Photon: $E = pc$ .
$\dfrac{K_e}{E} = \dfrac{v}{2c} = \dfrac{0.25}{2} = \dfrac{1}{8}$
So the answer is (c) $\frac{1}{8}$ .

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