The angular momentum of an electron revolving in a p-orbital is

Options

A. zero
B. `h//sqrt(2)pi`
C. `(h)/(2pi)`
D. `(1)/(2).(h)/(2pi)`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Orbital Type**:
The question specifies a p-orbital. In quantum mechanics, p-orbitals correspond to a specific azimuthal quantum number.

2. **Determine the Azimuthal Quantum Number (L)**:
For p-orbitals, the azimuthal quantum number \( L \) is equal to 1.

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

4. **Substitute the Value of L**:
Substitute \( L = 1 \) into the formula:
\[ L = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L = \sqrt{1 \cdot 2} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \]

5. **Rewrite the Expression**:
We can express this as:
\[ L = \frac{h \sqrt{2}}{2\pi} \]

6. **Final Answer**:
Thus, the angular momentum of an electron revolving in a p-orbital is:
\[ L = \frac{h \sqrt{2}}{2\pi} \]