The orbital angular momentum of an electron in 3s-orbital is :

Options

A. `+(1)/(2).(h)/(2pi)`
B. zero
C. `(h)/(2pi)`
D. `sqrt2.(h)/(2pi)`

Explanation

To find the orbital angular momentum of an electron in the 3s orbital, we can follow these steps:

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

### Step 2: Identify the Azimuthal Quantum Number for the 3s Orbital
For the s-orbital (which includes the 3s orbital), the azimuthal quantum number \( l \) is always 0. This is because:
- For s-orbitals, \( l = 0 \).

### Step 3: Substitute the Value of \( l \) into the Formula
Now, substituting \( l = 0 \) into the formula for orbital angular momentum:
\[ L = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} \]

### Step 4: Calculate the Value of \( L \)
Calculating the expression:
\[ L = \sqrt{0} \cdot \frac{h}{2\pi} = 0 \]

### Step 5: Conclusion
Thus, the orbital angular momentum of an electron in the 3s orbital is:
\[ L = 0 \]

### Final Answer
The orbital angular momentum of an electron in the 3s orbital is **0**.

---