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The ratio of de Broglie wavelength of an α particle and a proton accelerated from rest by the same potential is 1/(√m), the value of m is

Asked in JEE Main 29th Jan 2nd Shift 2023 · Accelerated through a potential difference

(1) 4
(2) 16
(3) 2
(4) 8

Answer: (4) 8

Step-by-step solution

λ=h/(√2mqV), so λ∝1/(√mq) at fixed V.

(λ_α)/(λₚ)=√(mₚqₚ)/(m_α q_α)=√1/(4×2)=1/(√8).

So m=8.

Why the other options are wrong

(1) comes from the mass ratio alone, leaving the charge out
(2) comes from squaring the correct factor
(3) comes from the charge ratio alone, leaving the mass out

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