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Q.

The energy of a I, II and III energy levels of a certain atom are E, $\frac{4 E}{3}$ and 2E respectively A photon of wavelength $λ$ is emitted during a transition from III to I. What will be the wavelength of emission for transition II to I?

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a

$\frac{λ}{2}$

b

$λ$

c

2 $λ$

d

3 $λ$

answer is D.

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Detailed Solution

For II to I transition
$ΔE = \frac{4 E}{3} - E = \frac{hc}{λ_{II \to I}}; \frac{E}{3} = \frac{hc}{λ_{II \to 1}}$
For III to I transition
$\begin{array}{l} ΔE = 2 E - E = \frac{hc}{λ_{III \to 1}} or E = \frac{hc}{λ} \\ ∴ \frac{hc}{3 \times λ} = \frac{hc}{λ_{II - I}}; λ_{II - I} = 3 λ \end{array}$

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