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Q.
Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \lambda_{1}/ \lambda_{2}$ , is given by
Atoms
Solution:
From energy level diagram, using $\Delta E = \frac{hc}{\lambda}$
For wavelength $\lambda_{1} \Delta E = -E-\left(-2E\right) = \frac{hc}{\lambda_{1}}$
$\therefore \lambda_{1}= \frac{hc}{E}$
For wavelength $\lambda_{2} \Delta E = - E -\left(-\frac{4E}{3}\right) = \frac{hc}{\lambda_{2}}$
$\therefore \lambda_{2} =\frac{hc}{\left(\frac{E}{3}\right)}$
$\therefore r = \frac{\lambda_{1}}{\lambda_{2}} = \frac{1}{3}$
