Question

Energy levels A, B and C of a certain atoms correspond to increasing values of every level i.e., $E_A<E_B<E_C$. If ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$ are the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, then 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 ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

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