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  4. The de Broglie wavelength of a proton and α -particle are equal. The ratio of their velocities is :

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Q. The de Broglie wavelength of a proton and $\alpha$ -particle are equal. The ratio of their velocities is :

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Solution:

$\lambda=\frac{ h }{ mv }$
$\lambda_{ P }=\lambda_{\alpha}$
$m _{ P } v _{ P }= m _{\alpha} v _{\alpha}$
$m _{ P } v _{ P }=4 m _{ p } v _{\alpha} \left( m _{\alpha}=4 m _{ P }\right)$
$\frac{ v _{ P }}{ v _{\alpha}}=4$