Q67 / 90 · JEE Main 2024 (05 Apr Shift 2) · Physics

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

A
r
Correct answer
B
$\sqrt{\mathrm{r}}$
C
$\frac{1}{\sqrt{\mathrm{r}}}$
D
$\frac{1}{\mathrm{r}}$

Solution

$\begin{aligned} & \mathrm{F}_{\mathrm{C}}=\frac{\mathrm{mv}^2}{\mathrm{r}} \\ & \frac{\mathrm{Kq}_1 \mathrm{q}_2}{\mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}} \\ & \mathrm{mv}^2 \mathrm{r}^2=K \mathrm{~K}_1 \mathrm{q}_2 \mathrm{r} \\ & \frac{\mathrm{L}^2}{\mathrm{~m}}=K \mathrm{Kq}_1 \mathrm{q}_2 \mathrm{r} \\ & \mathrm{L} \propto \sqrt{\mathrm{r}}\end{aligned}$

Hence, the correct answer is option: 'B'.

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