The orbital angular momentum of `3p` electron is :

Options

A. `sqrt(3)h`
B. `sqrt(6)h`
C. zero
D. `sqrt(2)(h)/(2pi)`

Answer

To find the orbital angular momentum of a 3p electron, we will follow these steps:

### Step 1: Identify the Azimuthal Quantum Number (l)
For a p electron, the azimuthal quantum number \( l \) is equal to 1. This is because:
- \( s \) electrons have \( l = 0 \)
- \( p \) electrons have \( l = 1 \)
- \( d \) electrons have \( l = 2 \)
- and so on.

### Step 2: Use the Formula for Orbital Angular Momentum
The formula for calculating the orbital angular momentum \( L \) is given by:
\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]
where \( h \) is Planck's constant.

### Step 3: Substitute the Value of l into the Formula
Now, substituting \( l = 1 \) into the formula:
\[ L = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L = \sqrt{1 \cdot 2} \cdot \frac{h}{2\pi} \]

### Step 4: Calculate the Result
Calculating the square root:
\[ L = \sqrt{2} \cdot \frac{h}{2\pi} \]

### Conclusion
Thus, the orbital angular momentum of a 3p electron is:
\[ L = \frac{\sqrt{2}h}{2\pi} \]

### Final Answer
The orbital angular momentum of the 3p electron is \( \frac{\sqrt{2}h}{2\pi} \).

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