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JEE Main 2023 (1 Feb, Shift 1) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2023 (1 Feb, Shift 1)

Q78JEE Main 2023 · 1 FEB · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$ . An alpha particle having certain kinetic energy has the same de-Broglie wavelength $\lambda$ . The ratio of kinetic energy of proton and that of alpha particle is:

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Answer: (c)

Same $\lambda$ means same momentum $p$ .
$K = \dfrac{p^2}{2m} \Rightarrow \dfrac{K_p}{K_\alpha} = \dfrac{m_\alpha}{m_p} = \dfrac{4m_p}{m_p} = 4$
So the answer is (c) $4:1$ .

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