Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e. $E_{A} < E_{B} < E_{C}$ . If $λ_{1}, λ_{2}, λ_{3}$ are the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct

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$λ_{3} = λ_{1} + λ_{2}$

$λ_{1} + λ_{2} + λ_{3} = 0$

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

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

answer is B.

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Detailed Solution

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

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