Question

Energy levels $A,B$ and $C$ of a certain atom corresponding to increasing values of energy i.e. $E_A<E_B<E_C$. If ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$ are wavelengths of radiations corresponding to transitions $C$ to $B,B$ to $A$ and $C$ to $A$ respectively, which of the following relations is correct?

• A. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
• B. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$
• C. ${\lambda }_3={\lambda }_1+{\lambda }_2$
• D. ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

Answer 1

Answer: (D)

As $E_C-E_A=E_C-E_B+E_B-E_A$
$\frac{hc}{{\lambda }_3}=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$
$\frac{1}{{\lambda }_3}=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$
$\therefore {\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$