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

Correct answer: A. 4: 1 λ = (h)/(mv) λ _ p = λ _ α m _ P V _ P = m _ α v _ α m _ P v _ P = 4 m _ p v _ α ( m _ α = 4 m _ P ) v _ p v _ α = 4

JEE Main 202124 FebruaryEvening Shift

Exam: JEE Main
Year: 2021
Date: 24 February
Shift: Evening Shift
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2021 · 24 February · Evening Shift · Physics · Dual Nature of Matter

The de Broglie wavelength of a proton and α -particle are equal....

The de Broglie wavelength of a proton and

\alpha

-particle are equal. The ratio of their velocities is

Options

A $4: 1$
B $4: 3$
C $1: 4$
D $4: 2$

Correct answer

A. $4: 1$

Step-by-step solution

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

$\dfrac{{v}_{p}}{{v}_{\alpha}} = 4$

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