Question

Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e. $E_{A} < E_{B} < E_{C}$. If $\lambda_{1},\mspace{6mu}\lambda_{2},\mspace{6mu}\lambda_{3}$are the wavelengths of radiations

corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct.

• A. $\lambda_{3} = \lambda_{1} + \lambda_{2}$
• B. $\lambda_{3} = \frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$
• C. $\lambda_{1} + \lambda_{2} + \lambda_{3} = 0$
• D. $\lambda_{3}^{2} = \lambda_{1}^{2} + \lambda_{2}^{2}$

Answer 1

Answer: (B)

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

Answer 2

Let the energy in A, B and C state be E_A. E_B and E_C, then from the figure

$\nu_{\text{Balmer}} = \frac{c}{\lambda_{\max}\left\lbrack \frac{1}{(2)^{2}} - \frac{1}{(3)^{2}} \right\rbrack\frac{5RC}{36}}$or $\frac{hc}{\lambda_{1}} + \frac{hc}{\lambda_{2}} = \frac{hc}{\lambda_{3}}$

$\Rightarrow \lambda_{3} = \frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$.