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. `2to1`
B. `3to2`
C. `4to2`
D. `4to3`

Explanation

To determine the transitions that result in infrared radiation in a hydrogen-like atom, we need to understand the different series of spectral lines associated with electron transitions between energy levels.

### Step-by-Step Solution:

1. **Identify the Series**:
- The transitions of electrons in a hydrogen-like atom can be categorized into different series based on the final energy level (n_final):
- **Lyman Series**: n_final = 1 (Ultraviolet radiation)
- **Balmer Series**: n_final = 2 (Visible radiation)
- **Paschen Series**: n_final = 3 (Infrared radiation)
- **Brackett Series**: n_final = 4 (Infrared radiation)
- **Pfund Series**: n_final = 5 (Infrared radiation)

2. **Determine the Required Transition for Infrared Radiation**:
- Infrared radiation is produced when the electron transitions to the n = 3, n = 4, or n = 5 energy levels. Therefore, we need to find transitions where the final state (n_final) is either 3, 4, or 5.

3. **Identify Possible Transitions**:
- For infrared radiation:
- Transition from n_initial = 4 to n_final = 3 (Paschen Series)
- Transition from n_initial = 5 to n_final = 4 (Brackett Series)
- Transition from n_initial = 6 to n_final = 5 (Pfund Series)

4. **Conclusion**:
- The transitions that yield infrared radiation in a hydrogen-like atom are:
- From n = 4 to n = 3 (Paschen Series)
- From n = 5 to n = 4 (Brackett Series)
- From n = 6 to n = 5 (Pfund Series)

### Final Answer:
Infrared radiation will be obtained in the transitions from n = 4 to n = 3 (Paschen Series), n = 5 to n = 4 (Brackett Series), or n = 6 to n = 5 (Pfund Series).

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