The wavelengths and frequencies of photon in transitions 1,2 and 3 for hydrogen like atom are $\lamb

Question

The wavelengths and frequencies of photon in transitions 1,2 and 3 for hydrogen like atom are $\lambda_1, \lambda_2, \lambda_3, v_1, v_2$ and $v_3$ respectively. Then :

Professor PC Thomas Classes · Answer

(a): We use $\Delta E_3=\Delta E_1+\Delta E_2$ \ $ \begin{aligned} & h v_3=h v_1+h v_2 \ & \Rightarrow v_3=v_1+v_2 \ & \Rightarrow \frac{c}{\lambda_3}=\frac{c}{\lambda_1}+\frac{c}{\lambda_2} \Rightarrow \lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2} \end{aligned} $