In a hypothetical atom, if transition from `n=4` to `n=3` produces visible light then the possible transition to obtain infrared radiation is:

Options

A. n=5 to n=3
B. n=4 to n=2
C. n=3 to n=1
D. n=5 to n=4

Answer

To solve the problem, we need to analyze the transitions in the hypothetical atom and determine which transition produces infrared radiation based on the given information that the transition from \( n=4 \) to \( n=3 \) produces visible light.

### Step-by-Step Solution:

1. **Understanding Energy Levels**:
The energy of a photon emitted during a transition between two energy levels in an atom is given by the difference in energy between those levels. The higher the energy level, the more energy is required to transition to a lower level.

2. **Energy of the Visible Light Transition**:
We know that the transition from \( n=4 \) to \( n=3 \) produces visible light. Let's denote the energy of this transition as \( E \).

3. **Analyzing the Options**:
We will analyze each option to see if the transition results in a photon with energy less than that of the visible light photon \( E \).

- **Option 1: Transition from \( n=5 \) to \( n=3 \)**:
- The energy difference for this transition will be greater than that of the transition from \( n=4 \) to \( n=3 \) because the electron is moving from a higher energy level (5) to a lower one (3). Thus, \( E_1 > E \). This cannot produce infrared radiation.

- **Option 2: Transition from \( n=4 \) to \( n=2 \)**:
- Similar to the first option, the energy difference here will also be greater than \( E \) because the electron is moving from \( n=4 \) to a much lower level \( n=2 \). Thus, \( E_2 > E \). This cannot produce infrared radiation.

- **Option 3: Transition from \( n=3 \) to \( n=1 \)**:
- Again, the energy difference for this transition will be greater than \( E \) since the electron is moving from \( n=3 \) to \( n=1 \). Thus, \( E_3 > E \). This cannot produce infrared radiation.

- **Option 4: Transition from \( n=5 \) to \( n=4 \)**:
- In this case, the electron is moving from \( n=5 \) to \( n=4 \). The energy difference here will be less than that of the transition from \( n=4 \) to \( n=3 \) because the energy levels are closer together as we move to higher levels. Thus, \( E_4 < E \). This transition can produce infrared radiation.

4. **Conclusion**:
The only transition that can produce infrared radiation is the transition from \( n=5 \) to \( n=4 \).

### Final Answer:
The possible transition to obtain infrared radiation is from \( n=5 \) to \( n=4 \).

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