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  4. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r=λ1 / λ2, is given by

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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 byPhysics Question Image

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Solution:

From energy level diagram, using $\Delta E=\frac{h c}{\lambda}$
For wavelength $\lambda_1 \Delta E=-E-(-2 E)=\frac{h c}{\lambda_1} $
$\therefore \lambda_1=\frac{h c}{E}$
For wavelength $\lambda_2 \Delta E=-E-\left(-\frac{4 E}{3}\right)=\frac{h c}{\lambda_2}$
$\therefore \lambda_2=\frac{h c}{\left(\frac{E}{3}\right)} $
$ \therefore r=\frac{\lambda_1}{\lambda_2}=\frac{1}{3}$