The transtion from the state `n = 4 to n = 3 ` in a hydrogen like atom results in ultraviolet radiation Infrared rediation will be obtained in the transition from :

Options

A. `2 rarr 1`
B. `3 rarr 2`
C. `4 rarr 2`
D. `5 rarr 4`

Answer

To solve the problem of determining which transition in a hydrogen-like atom results in infrared radiation, we can follow these steps:

### Step 1: Understand the Energy Levels
In a hydrogen-like atom, the energy levels are quantized and are given by the formula:
\[ E_n = -\frac{Z^2 \cdot 13.6 \, \text{eV}}{n^2} \]
where \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)), and \( n \) is the principal quantum number (1, 2, 3, ...).

### Step 2: Identify the Transition for Ultraviolet Radiation
The problem states that the transition from \( n = 4 \) to \( n = 3 \) results in ultraviolet (UV) radiation. This indicates that the energy difference between these two levels is significant enough to produce UV radiation.

### Step 3: Determine the Energy Difference for Infrared Radiation
Infrared (IR) radiation corresponds to transitions with smaller energy differences. The transitions that typically produce IR radiation are those that involve lower energy levels, specifically transitions from higher levels to lower levels, but not too low.

### Step 4: Analyze Possible Transitions
To find transitions that result in IR radiation, we can consider transitions from:
- \( n = 3 \) to \( n = 2 \)
- \( n = 4 \) to \( n = 3 \) (already known to produce UV)
- \( n = 5 \) to \( n = 4 \)
- \( n = 5 \) to \( n = 3 \)
- \( n = 6 \) to \( n = 5 \)

Among these, the transition from \( n = 4 \) to \( n = 3 \) is already producing UV radiation. Therefore, we need to look for transitions involving \( n = 5 \) or higher to lower states.

### Step 5: Identify the Correct Transition
The transition from \( n = 5 \) to \( n = 4 \) is a suitable candidate for producing infrared radiation since it involves a smaller energy difference compared to transitions that produce UV radiation.

### Conclusion
The transition that results in infrared radiation in a hydrogen-like atom is from \( n = 5 \) to \( n = 4 \).

### Final Answer
**Infrared radiation will be obtained in the transition from \( n = 5 \) to \( n = 4 \).**

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