# The order of energies of energy levels, A, B and C is EA < EB < EC , if the wavelength corresponding to transitions...

Q: The order of energies of energy levels, A, B and C is EA < EB < EC , if the wavelength corresponding to transitions C → B, B → A and C → A are λ1 , λ2 and λ3 respectively , then which of the following relations is correct ?

(a) λ1 + λ2 + λ3 = 0

(b) λ32 = λ12 + λ22

(c) λ3 = λ1 + λ2

(d) $\displaystyle \lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$

Ans: (d)

Sol: ECA = ECB + EBA

$\displaystyle \frac{h c}{\lambda_3} = \frac{h c}{\lambda_1} + \frac{h c}{\lambda_2}$

$\displaystyle \frac{1}{\lambda_3} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$

$\displaystyle \lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$

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