\(E_C - E_B = \frac{hc}{\lambda_1}\) ......(1)
\(E_B - E_A = \frac{hc}{\lambda_2}\) ......(2)
\(E_C - E_A = \frac{hc}{\lambda_3}\) ......(3)
Adding (1) and (2), we have
\(E_C - E_A = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}\) .......(4)
From (3) and (4), we have
\(\frac{hc}{\lambda_3} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}\)
⇒ \(\frac 1{\lambda_3} = \frac1{\lambda_1} +\frac 1{\lambda_2}\)
⇒ \(\frac 1{\lambda_3} = \frac{\lambda_1+ \lambda_2}{\lambda_1\lambda_2}\)
⇒ \({\lambda_3} = \frac{\lambda_1\lambda_2}{\lambda_1+ \lambda_2}\)
