Orbital angular momentum of 3s and 3p are :

Options

A. `(h)/(2pi) , (h)/(2pi)`
B. `(h)/(sqrt2 pi) , (h)/(sqrt2 pi)`
C. `0 , (sqrt(2h))/(pi)`
D. `0 , (h)/(sqrt2 pi)`

Answer

To find the orbital angular momentum of the 3s and 3p orbitals, we need to follow these steps:

### Step 1: Identify the quantum numbers
- For the 3s orbital, the azimuthal quantum number \( l \) is 0 (since 's' corresponds to \( l = 0 \)).
- For the 3p orbital, the azimuthal quantum number \( l \) is 1 (since 'p' corresponds to \( l = 1 \)).

### Step 2: Calculate the orbital angular momentum
The formula for the orbital angular momentum \( L \) is given by:
\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]

### Step 3: Calculate for 3s
- For 3s, \( l = 0 \):
\[ L_{3s} = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} = \sqrt{0} \cdot \frac{h}{2\pi} = 0 \]

### Step 4: Calculate for 3p
- For 3p, \( l = 1 \):
\[ L_{3p} = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} = \sqrt{1 \cdot 2} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \]

### Step 5: Final results
- The orbital angular momentum for 3s is \( 0 \).
- The orbital angular momentum for 3p is \( \sqrt{2} \cdot \frac{h}{2\pi} \).

### Conclusion
Thus, the orbital angular momentum of 3s is \( 0 \) and for 3p it is \( \sqrt{2} \cdot \frac{h}{2\pi} \).