Question

What is the angular momentum for $p$-shell electron ?

• A. $\frac{3\mathrm{h}}{\mathrm{\pi }}$
• B. Zero
• C. $\frac{\sqrt{2}\mathrm{h}}{2\mathrm{\pi }}$
• D. none

Answer 1

The correct option is C

$\frac{\sqrt{2}\mathrm{h}}{2\mathrm{\pi }}$

Explanation for correct option

(C) $\frac{\sqrt{\mathbf{2}}\mathbf{h}}{\mathbf{2}\mathbf{\pi }}$

Bohr's Model of a Hydrogen Atom

• According to the Bohr model, electrons orbit the nucleus with set energy levels.
• Orbits farther from the nucleus have higher energy levels.
• Electrons emit energy in the form of light when they return to a lower energy state.
• Bohr gave the postulates to define the angular momentum of the electrons.

Angular momentum

• Angular momentum is represented by $\mathrm{L}$.
• Formula for calculating angular momentum is as follows:
• $\mathrm{L}=\sqrt{\mathrm{l}(\mathrm{l}+1)}\frac{\mathrm{h}}{2\mathrm{\pi }\mathrm{}}$ ,
• $\mathrm{l}$ is Azimuthal quantum number.
• $\mathrm{h}$ is the Planck's constant.

Angular momentum for $\mathit{p}\mathbf{-}$shell

• For $p-$shell value of $\mathrm{l}$ is $1$.
• The angular momentum is as follows:

$\begin{array}{rcl}\mathrm{L}& =& \sqrt{\mathrm{l}(\mathrm{l}+1)}\frac{\mathrm{h}}{2\mathrm{\pi }\mathrm{}}\\ & =& \sqrt{1(1+1)}\frac{\mathrm{h}}{2\mathrm{\pi }\mathrm{}}\\ & =& \frac{\sqrt{2}\mathrm{h}}{2\mathrm{\pi }\mathrm{}}\end{array}$

Explanation for incorrect options

• The angular momentum for $p$-shell electron is $\frac{\sqrt{2}\mathrm{h}}{2\mathrm{\pi }}$.
• Hence, all other options (A), (B) and (D) are incorrect.

Therefore, the correct option is (C) $\frac{\sqrt{\mathbf{2}}\mathbf{h}}{\mathbf{2}\mathbf{\pi }}$.