The angular momentum of an electron in `4s` orbital, `3p` orbitals and `4th` orbit are

Options

A. `0,(1)/(sqrt(2)) (h)/(pi),(2h)/(pi)`
B. `(1)/(sqrt(2)) (h)/(2),(2h)/(pi),0`
C. `0,(sqrt(2)h)/(pi) ,(4h)/(pi)`
D. `(sqrt(2h))/(pi), (4h)/(pi),0`

Answer

To find the angular momentum of an electron in the 4s orbital, 3p orbital, and the 4th orbit, we can use the following principles:

### Step 1: Angular Momentum in the 4th Orbit
According to Bohr's model, the angular momentum (L) of an electron in the nth orbit is given by the formula:

\[ L = \frac{nh}{2\pi} \]

For the 4th orbit (n = 4):

\[ L = \frac{4h}{2\pi} = \frac{2h}{\pi} \]

### Step 2: Angular Momentum in the 4s Orbital
The angular momentum for orbitals can also be calculated using the azimuthal quantum number (l). The formula for orbital angular momentum is:

\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]

For the 4s orbital, the azimuthal quantum number \( l = 0 \):

\[ L = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} = 0 \]

### Step 3: Angular Momentum in the 3p Orbital
For the 3p orbital, the azimuthal quantum number \( l = 1 \):

\[ L = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \]

### Summary of Results
- Angular momentum in the 4th orbit: \( \frac{2h}{\pi} \)
- Angular momentum in the 4s orbital: \( 0 \)
- Angular momentum in the 3p orbital: \( \frac{\sqrt{2}h}{2\pi} \)