The change in orbital angular momentum corresponding to an electron transition inside a hydrogen atom can be-

Options

A. `(h)/(2pi)`
B. `(h)/(pi)`
C. `(h)/(2pi)`
D. `(h)/(8pi)`

Explanation

To solve the problem regarding the change in orbital angular momentum corresponding to an electron transition inside a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Orbital Angular Momentum**:
The orbital angular momentum (OAM) 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), and \( h \) is Planck's constant.

2. **Identify the Transition**:
When an electron transitions from an initial state \( n_1 \) to a final state \( n_2 \), we need to calculate the change in orbital angular momentum (\( \Delta L \)):
\[ \Delta L = L_{n_2} - L_{n_1} \]

3. **Substituting the Values**:
Substitute the values of \( L \) for both states:
\[ \Delta L = n_2 \frac{h}{2\pi} - n_1 \frac{h}{2\pi} \]
This simplifies to:
\[ \Delta L = \left(n_2 - n_1\right) \frac{h}{2\pi} \]

4. **Analyzing the Change**:
The term \( n_2 - n_1 \) is the difference in the principal quantum numbers, which is an integer. Therefore, \( \Delta L \) can be expressed as:
\[ \Delta L = k \frac{h}{2\pi} \]
where \( k = n_2 - n_1 \) is an integer.

5. **Evaluating the Options**:
Now, we need to evaluate the options given in the question:
- \( \frac{h}{4\pi} \) - This is not a multiple of \( \frac{h}{2\pi} \) (as \( \frac{1}{4} \) is not an integer).
- \( \frac{h}{\pi} \) - This can be expressed as \( 2 \cdot \frac{h}{2\pi} \) (where 2 is an integer).
- \( \frac{h}{2\pi} \) - This is \( 1 \cdot \frac{h}{2\pi} \) (where 1 is an integer).
- \( \frac{h}{8\pi} \) - This is not a multiple of \( \frac{h}{2\pi} \) (as \( \frac{1}{8} \) is not an integer).

6. **Conclusion**:
The correct answers are \( \frac{h}{\pi} \) and \( \frac{h}{2\pi} \) since they correspond to integer multiples of \( \frac{h}{2\pi} \).

### Final Answer:
The change in orbital angular momentum corresponding to an electron transition inside a hydrogen atom can be \( \frac{h}{\pi} \) and \( \frac{h}{2\pi} \).