When electron jumps from n=4 level to n=1 level,the angular momentum of electron changes by

Options

A. `h/(2pi)`
B. `(2h)/(2pi)`
C. `(3h)/(2pi)`
D. `(4h)/(2pi)`

Answer

To solve the problem of how the angular momentum of an electron changes when it jumps from the n=4 level to the n=1 level, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Momentum in Quantum Mechanics**:
The angular momentum (L) of an electron in a given orbit is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

2. **Calculate Angular Momentum at n=1**:
For the electron at the n=1 level:
\[ L_1 = 1 \cdot \frac{h}{2\pi} = \frac{h}{2\pi} \]

3. **Calculate Angular Momentum at n=4**:
For the electron at the n=4 level:
\[ L_4 = 4 \cdot \frac{h}{2\pi} = \frac{4h}{2\pi} \]

4. **Determine the Change in Angular Momentum**:
The change in angular momentum (\( \Delta L \)) when the electron jumps from n=4 to n=1 is calculated as:
\[ \Delta L = L_4 - L_1 \]
Substituting the values we calculated:
\[ \Delta L = \frac{4h}{2\pi} - \frac{h}{2\pi} = \frac{4h - h}{2\pi} = \frac{3h}{2\pi} \]

5. **Final Answer**:
Therefore, the change in angular momentum when the electron jumps from n=4 to n=1 is:
\[ \Delta L = \frac{3h}{2\pi} \]

### Conclusion:
The change in angular momentum of the electron is \( \frac{3h}{2\pi} \).