Question

For a certain atom, there are energy levels $A,B,C$ of a certain atom corresponds to increasing values of energy, $i.e.,E_A<E_B<E_C$. Choose the correct option 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 :

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

As we know,
$E=hv=\frac{hc}{\lambda }$

$E_3-E_1=(E_3-E_2)+(E_2-E_1)$

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

$\frac{1}{{\lambda }_3}=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$

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

Hence, the correct option is $B$