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

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

$λ_{3}$ = $λ_{1}$ + $λ_{2}$

$λ_{3}^{2} = λ_{1}^{2} + λ_{2}^{2}$

$λ_{1}$ + $λ_{2}$ + $λ_{3}$ = 0

answer is B.

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Detailed Solution

Let energy corresponding to state A, B and C be
E_A, E_B and E_C respectively.
So, from energy level diagram,

$(E_{C} - E_{B}) + (E_{B} - E_{A}) = (E_{C} - E_{A})$

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

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