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

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Q. 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-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

JEE MainJEE Main 2023Dual Nature of Radiation and Matter

Solution:

$K E=\frac{p^2}{2 m}=\frac{h^2}{2 m \lambda^2} $
$ \frac{K E_p}{K E_\alpha}=\frac{m_\alpha}{m_p}=4: 1$