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JEE Main levelSingle correct optionDifficulty 2 of 3as124

A proton and an $α$ -particle (mass $4$ times that of a proton, charge $2 e$ ) are accelerated from rest through the same potential difference. The ratio $λ_{p} / λ_{α}$ is

A $0.5$
B $4$
C $2.828$
D $2$

Answer: C

λ = h / 2 m q V

, so

λ \propto 1/ m q

. Then

λ_{p} / λ_{α} = (4 \times 2) / (1 \times 1) = 8 = 2.828

.

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