Energy levels A, B, C of a certain atom corre | vedclass

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(B) Let the energies of the states $A, B,$ and $C$ be $E_A, E_B,$ and $E_C$ respectively.From the principle of conservation of energy,the energy of th

Vedclass · Accepted Answer

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

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(B) Let the energies of the states $A, B,$ and $C$ be $E_A, E_B,$ and $E_C$ respectively.From the principle of conservation of energy,the energy of the transition from $C$ to $A$ is equal to the sum of the energies of the transitions from $C$ to $B$ and $B$ to $A$.Thus,$(E_C - E_A) = (E_C - E_B) + (E_B - E_A)$.Using the relation $E = \frac{hc}{\lambda}$,we can write:$\frac{hc}{\lambda_3} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}$Dividing both sides by $hc$,we get:$\frac{1}{\lambda_3} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$$\frac{1}{\lambda_3} = \frac{\lambda_1 + \lambda_2}{\lambda_1 \lambda_2}$Therefore,$\lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$.

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