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  4. A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λp and λα are in the ratio,

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Q. A proton and an $\alpha$-particle are accelerated from rest to the same energy. The de Broglie wavelengths $\lambda_{p}$ and $\lambda_{\alpha}$ are in the ratio,

NEETNEET 2019Dual Nature of Radiation and Matter

Solution:

$\lambda = \frac{h}{\sqrt{2mE_k}} \,\,(\because E_k$ is same for both)
$\Rightarrow \frac{\lambda_p}{\lambda_{\alpha}} = \sqrt{\frac{4m}{m}} $
$= 2 : 1$