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Explanation for the Correct Answer
1. Understanding the Wavelength Regions
In hydrogen-like atoms, electronic transitions between higher and lower energy levels emit electromagnetic radiation of specific wavelengths. The wavelength region (infrared (IR), visible, ultraviolet (UV), etc.) depends on the energy difference between the initial and final states.
2. Given Transition and Its Implication
It is stated that the transition from $n=4$ to $n=3$ results in ultraviolet (UV) radiation. Generally, larger energy gaps correspond to higher frequency (or shorter wavelength) radiation, such as UV, while smaller energy gaps correspond to longer wavelength radiation, such as IR.
3. Identifying an Infrared Transition
Infrared (IR) radiation has lower energy (longer wavelength) compared to ultraviolet (UV). Thus, to obtain IR radiation, the energy difference between the initial and final levels must be smaller than that between $n=4$ and $n=3$.
4. Checking the Options
Among the given transitions:
$3 \to 2$
$4 \to 2$
$5 \to 4$
$2 \to 1$
The option $5 \to 4$ has a smaller energy difference compared to $4 \to 3$, making it more likely to lie in the infrared region. Hence, moving from $n=5$ to $n=4$ is best associated with IR emission among the provided choices.
5. Conclusion
Therefore, the transition that gives infrared radiation is $n=5$ to $n=4$, matching the correct answer.
