Question

Identify the angular momentum which is not possible for an electron in Bohr's orbit of a hydrogen atom.

• A. $\frac{\mathrm{h}}{\mathrm{\pi }}$
• B. $\frac{3\mathrm{h}}{2\mathrm{\pi }}$
• C. $\frac{4\mathrm{h}}{\mathrm{\pi }}$
• D. $\frac{3\mathrm{h}}{4\mathrm{\pi }}$

Answer 1

The correct option is D

$\frac{3\mathrm{h}}{4\mathrm{\pi }}$

Explanation of the Correct option: (d)

1. Angular momentum of an electron (or any rotating substance) is the velocity of its rotation around an axis.
2. According to Bohr, angular momentum is expressed as-

$\mathrm{Angular}\mathrm{momentum}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$

where n is the orbit in which the electron is present and can have only the whole number.

h is the Plank's constant (= 6.626$\times$10^-34 Js.)

$\mathrm{\pi }$ is pi (=3.14)

3. If $\frac{3\mathrm{h}}{4\mathrm{\pi }}$ is factories, we get$\frac{3}{2}\times \frac{\mathrm{h}}{2\mathrm{\pi }}$. Thus, as per this n should be $\frac{3}{2}$ but it is not possible as n is always a whole number.

4. Hence, the angular momentum which is not possible for an electron in Bohr's orbit of a hydrogen atom is d)$\frac{3\mathrm{h}}{4\mathrm{\pi }}$.

The explanation for the incorrect option:

Option a)

If n = 2, then angular momentum is-

$\mathrm{Angular}\mathrm{momentum}=\frac{2\mathrm{h}}{2\mathrm{\pi }}=\frac{\mathrm{h}}{\mathrm{\pi }}$

Option b)

If n = 3, then angular momentum is-

$\mathrm{Angular}\mathrm{momentum}=\frac{3\mathrm{h}}{2\mathrm{\pi }}$

Option c)

If n = 8, then angular momentum is-

$\mathrm{Angular}\mathrm{momentum}=\frac{8\mathrm{h}}{2\mathrm{\pi }}=\frac{4\mathrm{h}}{\mathrm{\pi }}$

Conclusion: The correct option is d).