Physics · Atomic Physics

JEE Main 2024 — 5 April, Shift 2 — Question 33

The angular momentum of an electron in a hydrogen atom is proportional to : (Where $r$ is the radius of orbit of electron)

Option A:
$\sqrt{\mathrm{r}}$
Correct
Option B:
$\frac{1}{r}$
Option C:
R
Option D:
$\frac{1}{\sqrt{\mathrm{r}}}$

Answer: A

Step-by-step solution

$\quad \mathrm{F}_{\mathrm{C}}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$

$\frac{\mathrm{Kq}_{1} \mathrm{q}_{2}}{\mathrm{r}^{2}}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$ $\mathrm{mv}^{2} \mathrm{r}^{2}=\mathrm{Kq}_{1} \mathrm{q}_{2} \mathrm{r}$

$\frac{L^{2}}{\mathrm{~m}}=\mathrm{Kq}_{1} \mathrm{q}_{2} \mathrm{r}$

$\mathrm{L} \propto \sqrt{\mathrm{r}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Physics
Chapter: Atomic Physics
Topic: Rutherford's and Bohr's Model of Atom

Answer: A

Step-by-step solution

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