Q. Energy levels A, B, C of a certain atom corresponding to increasing values of energy, $i.e.,\ E_{A} < E_{B} < E_{C}.$ If $\lambda_{1},\lambda_{2},\lambda_{3}$ are the wavelength 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) $\lambda_{3}^{2} = \lambda_{1}^{2} + \lambda_{2}^{2}$
Explanation
(b) Let the energy in $A,B$ and $C$ states be $E_{A}.E_{B}$ and $E_{C}$, then from the figure
$\left( E_{C} - E_{B} \right) + \left( E_{B} - E_{A} \right) = (E_{C} - E_{A})$ or $\frac{hc}{\lambda_{1}} + \frac{hc}{\lambda_{2}} = \frac{hc}{\lambda_{3}}$
$\Rightarrow \lambda_{3} = \frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.