The orbital angular momentum of a p-electron is given as :

Options

A. `sqrt3(h)/(2pi)`
B. `sqrt((3)/(2))(h)/(pi)`
C. `sqrt6.sqrt((h)/(2pi))`
D. `(h)/(sqrt2pi)`

Explanation

To find the orbital angular momentum of a p-electron, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Orbital Angular Momentum**:
The formula for the orbital angular momentum (L) of an electron is given by:
\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]
where \( l \) is the azimuthal quantum number and \( h \) is Planck's constant.

2. **Identify the Value of \( l \) for a p-electron**:
For p-orbitals, the azimuthal quantum number \( l \) is equal to 1.

3. **Substitute the Value of \( l \) into the Formula**:
Substitute \( l = 1 \) into the formula:
\[ L = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} \]

4. **Simplify the Expression**:
Calculate \( 1 + 1 \):
\[ L = \sqrt{1 \cdot 2} \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L = \sqrt{2} \cdot \frac{h}{2\pi} \]

5. **Final Expression**:
Therefore, the orbital angular momentum of a p-electron is:
\[ L = \frac{h \sqrt{2}}{2\pi} \]