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Energy levels A, B, C of a certain atom correspond to increasing values of energy, i.e., $E_{A} < E_{B} < E_{C}$ . if $λ_{1}, λ_{2}, λ_{3}$ are the wavelengths of radiation corresponding to the transitions $C \to B$ , $B \to A$ and $C \to A$ respectively then

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$λ_{3} = λ_{1} + λ_{2}$

$λ_{3} + λ_{1} + λ_{2} = 0$

$λ_{3}^{2} = λ_{1}^{2} + λ_{2}^{2}$

$λ_{3} = \frac{λ_{1} λ_{2}}{λ_{1} + λ_{2}}$

answer is B.

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Detailed Solution

$\frac{h c}{λ_{3}} = \frac{h c}{λ_{2}} + \frac{h c}{λ_{1}}$

$∴ λ_{3} = \frac{λ_{1} λ_{2}}{λ_{1} + λ_{2}}$

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