The orbital angular momentum of an electron in `2s`-orbital is

Options

A. (a) Zero
B. (b) One
C. (c) Two
D. (d) Three

Answer

To find the orbital angular momentum of an electron in the 2s orbital, we can follow these steps:

### Step 1: Identify the Quantum Numbers
For the 2s orbital:
- The principal quantum number \( n = 2 \).
- The azimuthal quantum number \( l \) for an s orbital is always \( 0 \).

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

### Step 3: Substitute the Value of \( l \)
Substituting \( l = 0 \) into the formula:
\[ L = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L = \sqrt{0} \cdot \frac{h}{2\pi} = 0 \]

### Step 4: Conclusion
Thus, the orbital angular momentum of an electron in the 2s orbital is:
\[ \text{Orbital Angular Momentum} = 0 \]

### Final Answer
The orbital angular momentum of an electron in the 2s orbital is **0**.

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