The transition from the state n = 4 to n = 3 in a hydrogen like atom… | JEE Main 2009 (AIEEE)

Q73JEE Main 2009 · AIEEEMedium

Transitions, Photon Emission & Excitation

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

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Answer: (c)

Infrared needs a photon of lower energy than the $4\to3$ (UV) photon.
$4\to3$ : $\frac{1}{9} - \frac{1}{16} = \frac{7}{144} \approx 0.049$
$3\to2$ : $0.139$ , $4\to2$ : $0.1875$ , $2\to1$ : $0.75$ are all larger; $5\to4$ : $\frac{1}{16} - \frac{1}{25} = \frac{9}{400} \approx 0.0225$ is smaller.
So the answer is (c) $5 \rightarrow 4$ .

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