Question

For certain atom,there are energy levels A,B,C corresponding to energy values $E_A<E_B<E_C$.Choose the correct option if ${\lambda }_1,{\lambda }_2,{\lambda }_3$ are the wavelengths of radiations corresponding to the transition from C to B,B to A and C to A respectively.

• 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. $3{\lambda }_2={\lambda }_3+2{\lambda }_2$

Answer 1

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

From the diagram, we easily see that:
$E_{CA}=E_{BC}+E_{BA}$

$\Rightarrow \frac{hC}{{\lambda }_3}=\frac{hC}{{\lambda }_1}+\frac{hC}{{\lambda }_2}$

$\Rightarrow {\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$