The transition form the state `n = 3` to `n = 1` in a hydrogen-like atom results in ultraviolet radiation. Infared radiation will be obtained in the transition from

Options

A. `2 rarr 1`
B. `3 rarr 2`
C. `4 rarr 2`
D. `4 rarr 3`

Explanation

To solve the problem, we need to determine the transition in a hydrogen-like atom that results in infrared radiation. We know that the transition from \( n = 3 \) to \( n = 1 \) results in ultraviolet radiation. Let's analyze the possible transitions:

1. **Understanding the Series**:
- The transitions in hydrogen-like atoms can be classified into series based on the principal quantum numbers involved in the transitions.
- The main series are:
- **Lyman series**: Transitions to \( n = 1 \) (ultraviolet)
- **Balmer series**: Transitions to \( n = 2 \) (visible light)
- **Paschen series**: Transitions to \( n = 3 \) (infrared)
- **Brackett series**: Transitions to \( n = 4 \) (infrared)
- **Pfund series**: Transitions to \( n = 5 \) (far infrared)

2. **Identifying Infrared Transitions**:
- Infrared radiation is produced by transitions to \( n = 3 \) or higher levels.
- Specifically, the Paschen series (transitions to \( n = 3 \)) will yield infrared radiation.

3. **Finding the Transition**:
- The transition that produces infrared radiation can be from \( n = 4 \) to \( n = 3 \), \( n = 5 \) to \( n = 3 \), or any higher level down to \( n = 3 \).
- The simplest transition that results in infrared radiation is \( n = 4 \) to \( n = 3 \).

4. **Conclusion**:
- Therefore, the transition that results in infrared radiation is from \( n = 4 \) to \( n = 3 \).

### Final Answer:
The transition that results in infrared radiation is from \( n = 4 \) to \( n = 3 \).

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