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 ${\lambda }_1,{\lambda }_2,{\lambda }_3$ 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

The correct option is B ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

Let the energy in A, B and C state be $E_A.E_{B}and{E}_C$, then from the figure

$(E_C-E_B)+(E_B-E_A)=(E_C-E_A)or\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}=\frac{hc}{{\lambda }_3}\Rightarrow {\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$