Q74 / 90 · JEE Main 2024 (04 Apr Shift 2) · Physics

According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text {th }}$ orbit of hydrogen atom is:

A
$\frac{h}{\pi}$
B
$\frac{h}{2 \pi}$
C
$8 \frac{h}{\pi}$
Correct answer
D
$2 \frac{h}{\pi}$

Solution

Moment of momentum is $\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{P}}$ $\begin{aligned} & \overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} \times \mathrm{m} \overrightarrow{\mathrm{v}} \\ & \mathrm{L}=\mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi}=\frac{4 \mathrm{~h}}{2 \pi}=\frac{2 \mathrm{~h}}{\pi} \end{aligned}$

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

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