Transitions between three energy levels in a | vedclass

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(C) From the energy level diagram,the energy of the emitted photon is given by $\Delta E = \frac{hc}{\lambda}$.For the transitions shown:$1$) Transiti

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$\frac{1}{\lambda_1} = \frac{1}{\lambda_2} + \frac{1}{\lambda_3}$

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(C) From the energy level diagram,the energy of the emitted photon is given by $\Delta E = \frac{hc}{\lambda}$.For the transitions shown:$1$) Transition from $E_3$ to $E_1$ corresponds to wavelength $\lambda_1$: $E_3 - E_1 = \frac{hc}{\lambda_1} \quad (1)$$2$) Transition from $E_2$ to $E_1$ corresponds to wavelength $\lambda_2$: $E_2 - E_1 = \frac{hc}{\lambda_2} \quad (2)$$3$) Transition from $E_3$ to $E_2$ corresponds to wavelength $\lambda_3$: $E_3 - E_2 = \frac{hc}{\lambda_3} \quad (3)$We observe that $(E_3 - E_1) = (E_3 - E_2) + (E_2 - E_1)$.Substituting the expressions from equations $(1), (2),$ and $(3)$:$\frac{hc}{\lambda_1} = \frac{hc}{\lambda_3} + \frac{hc}{\lambda_2}$Dividing both sides by $hc$,we get:$\frac{1}{\lambda_1} = \frac{1}{\lambda_2} + \frac{1}{\lambda_3}$

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