Question

Energy levels $\text{P, Q, R}$ of an atom are shown below.
If $E_P<E_Q<E_R,$ then correct statements of the following is-

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

Answer 1

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



From the figure, we get,

$E_{RP}=E_{RQ}+E_{QP}$

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

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

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

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.