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) λ_{3} = λ_{1} + λ_{2}

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

(c) λ_{1} + λ_{2} + λ_{3} = 0

(d) λ_{3}^{2} = λ_{1}^{2} + λ_{2}^{2}

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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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