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(D) From the energy level diagram,we use the relation $\Delta E = \frac{hc}{\lambda}$.For the transition corresponding to wavelength $\lambda_1$,the e

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$r = \frac{1}{3}$

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(D) From the energy level diagram,we use the relation $\Delta E = \frac{hc}{\lambda}$.For the transition corresponding to wavelength $\lambda_1$,the energy difference is $\Delta E_1 = -E - (-2E) = E$.Thus,$\frac{hc}{\lambda_1} = E$,which gives $\lambda_1 = \frac{hc}{E}$.For the transition corresponding to wavelength $\lambda_2$,the energy difference is $\Delta E_2 = -E - (-\frac{4}{3}E) = \frac{1}{3}E$.Thus,$\frac{hc}{\lambda_2} = \frac{E}{3}$,which gives $\lambda_2 = \frac{3hc}{E}$.The ratio $r = \frac{\lambda_1}{\lambda_2} = \frac{hc/E}{3hc/E} = \frac{1}{3}$.

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \frac{\lambda_1}{\lambda_2}$ is given by

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