Question

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by

Answer 1

Answer: 0.34

From energy level diagram, using $\Delta E=\frac{hc}{\lambda }$
For wavelength ${\lambda }_1\Delta E=-E-(-2E)=\frac{hc}{{\lambda }_1}$
$\therefore {\lambda }_1=\frac{hc}{E}$
For wavelength ${\lambda }_2\Delta E=-E-\left(-\frac{4E}{3}\right)=\frac{hc}{{\lambda }_2}$
$\therefore {\lambda }_2=\frac{hc}{\left(\frac{E}{3}\right)}$
$\therefore r=\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{3}$