For certain atom, there are energy levels A, B, C corresponding to energy values EA < EB < EC...

Q: For certain atom, there are energy levels A, B, C corresponding to energy values EA < EB < EC. Choose the correct option if λ1 , λ2, λ3 are the wavelength of radiations corresponding to the transition from C to B, B to A and C to A respectively:

(a) λ3 = λ1 + λ2

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

(c) λ1 + λ2 + λ3 = 0

(d) 3 λ2 = λ3 + 2 λ2

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} $