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Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy i.e., $E_A < E_B < E_C$. If ${\lambda _1},{\lambda _2},{\lambda _3}$ are the wavelengths of radiation corresponding to the transition $C$ to $B, B$ to $A$ and $C$ to $A$ respectively, which of the following relation is correct ?
${\lambda _3} = {\lambda _1} + {\lambda _2}$
${\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}$
${\lambda _1} + {\lambda _2} + {\lambda _3} = 0$
$\lambda _3^2 = \lambda _1^2 + \lambda _2^2$
Solution
${E_3} = {E_1} + {E_2}$
$\mathrm{hv}_{3}=\mathrm{hv}_{1}+\mathrm{hv}_{2} \Rightarrow \frac{1}{\lambda_{3}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}$
or $\lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$
