The de Broglie wavelengths of a proton and an α particle are λ and 2 λ respectively. The ratio of the velocities of proton and α particle will be :

Physics · Atomic Physics

JEE Main 2024 — 1 February, Shift 1 — Question 38

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2 \lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :

Option A:
$1: 8$
Option B:
$1: 2$
Option C:
$4: 1$
Option D:
$8: 1$
Correct

Answer: D

Step-by-step solution

$\lambda=\frac{h}{p}=\frac{h}{m v} \Rightarrow v=\frac{h}{m \lambda}$

\frac{\mathrm{v}_{\mathrm{p}}}{\mathrm{v}_{\alpha}}=\frac{\mathrm{m}_{\alpha}}{\mathrm{m}_{\mathrm{p}}} \times \frac{\lambda_{\alpha}}{\lambda_{\mathrm{p}}}

=4 \times 2=8

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Physics
Chapter: Atomic Physics
Topic: Dual Nature of Matter

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

Answer: D

Step-by-step solution

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