JEE Main · 2009 · 12 Apr 2009 · Offline · Modern Physics

The transition from the state

n = 4

n = 3

in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

(A) $2 \to 1$
(B) $3 \to 2$
(C) $4 \to 2$
(D) $5 \to 4$ ✓ Correct

Answer: (D)

Solution

The energy of an emitted photon is proportional to

\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}

, so the larger this difference the more energetic, and bluer, the radiation. The

4 \to 3

jump already lies in the ultraviolet, meaning infrared, which is less energetic, must come from a transition with an even smaller energy gap. Among the choices the jump with the smallest value of

\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}

is the one between the two highest and closest levels, giving the

5 \to 4

transition.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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