Energy levels A, B, C of a certain atom corresponding to increasing values of energy, i.e. , EA < EB< EC ....

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Q: Energy levels A, B, C of a certain atom corresponding to increasing values of energy, i.e. , EA < EB< EC . If  λ1, λ2, λ3 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

(a) λ3 = λ1 + λ2

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

(c) λ1 + λ2 + λ3 = 0

(d) λ32 = λ12 + λ22

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Ans: (b)
Sol: $ \displaystyle \Delta E = h \nu = \frac{h c}{\lambda} $

$ \displaystyle E_C – E_A = ( E_C – E_B ) + ( E_B – E_A ) $

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