The angular momentum of d electron is

Options

A. `(h)/(2pi)sqrt(6)`
B. `h sqrt(6)`
C. `h sqrt(2)`
D. `(h)/(2pi)sqrt(2)`

Explanation

To find the angular momentum of a d electron, we can follow these steps:

### Step 1: Understand the concept of angular momentum
Angular momentum (L) in quantum mechanics for an electron in an atom is given by the formula:
\[ L = \sqrt{l(l + 1)} \frac{h}{2\pi} \]
where:
- \( l \) is the azimuthal quantum number,
- \( h \) is Planck's constant.

### Step 2: Identify the azimuthal quantum number for d electrons
For d electrons, the azimuthal quantum number \( l \) is equal to 2. This is because:
- s orbitals have \( l = 0 \),
- p orbitals have \( l = 1 \),
- d orbitals have \( l = 2 \).

### Step 3: Substitute the value of \( l \) into the formula
Now, we substitute \( l = 2 \) into the angular momentum formula:
\[ L = \sqrt{2(2 + 1)} \frac{h}{2\pi} \]

### Step 4: Simplify the expression
Calculating inside the square root:
\[ L = \sqrt{2 \times 3} \frac{h}{2\pi} = \sqrt{6} \frac{h}{2\pi} \]

### Step 5: Write the final expression
Thus, the angular momentum of a d electron can be expressed as:
\[ L = \frac{h \sqrt{6}}{2\pi} \]

### Step 6: Alternative representation
This can also be written in terms of \( \hbar \) (h-bar), where \( \hbar = \frac{h}{2\pi} \):
\[ L = \hbar \sqrt{6} \]

### Final Answer
The angular momentum of a d electron is:
\[ L = \hbar \sqrt{6} \]

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