In an electron transition inside a hydrogen atom, orbital angular momentum may change by

Options

A. h
B. `h//pi`
C. `h//2pi`
D. `h//4pi`

Answer

To solve the problem of how the orbital angular momentum may change during an electron transition inside a hydrogen atom, we need to analyze the possible changes in angular momentum based on the quantum mechanical model of the hydrogen atom.

### Step-by-Step Solution:

1. **Understanding Orbital Angular Momentum**:
The orbital angular momentum \( L \) of an electron in a hydrogen atom is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number (an integer: \( n = 1, 2, 3, \ldots \)) and \( h \) is Planck's constant.

2. **Change in Orbital Angular Momentum**:
When an electron transitions from one energy level to another, the change in orbital angular momentum can be expressed as:
\[ \Delta L = L_f - L_i = n_f \frac{h}{2\pi} - n_i \frac{h}{2\pi} = (n_f - n_i) \frac{h}{2\pi} \]
where \( n_i \) and \( n_f \) are the initial and final quantum numbers, respectively.

3. **Possible Values for Change in Angular Momentum**:
The change in angular momentum \( \Delta L \) can take values that are integer multiples of \( \frac{h}{2\pi} \). Thus, the possible changes can be:
- \( \Delta L = 0 \)
- \( \Delta L = \frac{h}{2\pi} \)
- \( \Delta L = \frac{2h}{2\pi} = \frac{h}{\pi} \)
- \( \Delta L = \frac{3h}{2\pi} \), and so on.

4. **Evaluating the Given Options**:
Now, let's evaluate the options provided in the question:
- **Option 1**: \( \frac{h}{\pi} \) - This is possible when \( n_f - n_i = 2 \) (e.g., from \( n = 3 \) to \( n = 1 \)).
- **Option 2**: \( \frac{h}{2\pi} \) - This is possible when \( n_f - n_i = 1 \) (e.g., from \( n = 2 \) to \( n = 1 \)).
- **Option 3**: \( h \) - This is not possible because it would require \( n_f - n_i = 4 \) which is not a valid transition in one step.
- **Option 4**: \( \frac{h}{4\pi} \) - This is also not possible as it would imply a non-integer value of \( n \).

5. **Conclusion**:
The only possible changes in orbital angular momentum during an electron transition in a hydrogen atom are \( \frac{h}{2\pi} \) and \( \frac{h}{\pi} \). Therefore, the correct answers are:
- \( \frac{h}{2\pi} \) and \( \frac{h}{\pi} \).

### Final Answer:
The orbital angular momentum may change by \( \frac{h}{2\pi} \) and \( \frac{h}{\pi} \).