The angular momentum of electrons in d orbital is equal to

Options

A. `sqrt(6)h`
B. `sqrt(2)h`
C. `2sqrt(3)h`
D. 0 h

Explanation

To find the angular momentum of electrons in a d orbital, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Azimuthal Quantum Number for d Orbital**:
For the d orbital, the azimuthal quantum number \( l \) is equal to 2.

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

4. **Calculate the Expression Inside the Square Root**:
First, calculate \( 2 + 1 = 3 \), then:
\[ L = \sqrt{2 \times 3} \frac{h}{2\pi} \]
This simplifies to:
\[ L = \sqrt{6} \frac{h}{2\pi} \]

5. **Final Expression for Angular Momentum**:
Therefore, the angular momentum of electrons in the d orbital is:
\[ L = \sqrt{6} \frac{h}{2\pi} \]

### Conclusion:
The angular momentum of electrons in the d orbital is equal to \( \sqrt{6} \frac{h}{2\pi} \).

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