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JEE Main 2025 (28 Jan, Shift 1) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2025 (28 Jan, Shift 1)

Q38JEE Main 2025 · 28 JAN · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

A proton of mass ' $m_P$ ' has same energy ' $E$ ' as that of a photon of wavelength ' $\lambda$ '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

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Answer: (d)

Proton: $\lambda_{dB} = \dfrac{h}{\sqrt{2m_pE}}$ . Photon: $\lambda = \dfrac{hc}{E}$ .
$\dfrac{\lambda_{dB}}{\lambda} = \dfrac{E}{c\sqrt{2m_pE}} = \dfrac{1}{c}\sqrt{\dfrac{E}{2m_p}}$
So the answer is (d).

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