Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e. $E_A<E_B<E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct.

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

Let the energy in A, B and C state be E_A. E_B and E_C, then from the figure.

$\left(E_C-E_B\right)+\left(E_B-E_A\right)=\left(E_C-E_A\right)$ or $\frac{h c}{\lambda_1}+\frac{h c}{\lambda_2}=\frac{h c}{\lambda_3}$

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