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(C) The energy difference between two levels is related to the wavelength of the emitted photon by the relation $\Delta E = \frac{hc}{\lambda}$.For th

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$\lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$

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(C) The energy difference between two levels is related to the wavelength of the emitted photon by the relation $\Delta E = \frac{hc}{\lambda}$.For the given transitions:$1$. Transition from $C$ to $B$: $E_C - E_B = \frac{hc}{\lambda_1}$$2$. Transition from $B$ to $A$: $E_B - E_A = \frac{hc}{\lambda_2}$$3$. Transition from $C$ to $A$: $E_C - E_A = \frac{hc}{\lambda_3}$From the energy level diagram,we can see that:$(E_C - E_A) = (E_C - E_B) + (E_B - E_A)$Substituting the energy expressions in terms of wavelength:$\frac{hc}{\lambda_3} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}$Dividing both sides by $hc$:$\frac{1}{\lambda_3} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$$\frac{1}{\lambda_3} = \frac{\lambda_2 + \lambda_1}{\lambda_1 \lambda_2}$Therefore,$\lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$.

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