Physics - Modern Physics Question with Solution | TestHub

Minimum wavelength for Balmer series, $\begin{array}{rl}& \frac{1}{{\lambda }_{\min B}}=R\left(\frac{1}{2^2}-\frac{1}{{\infty }^2}\right)\\ & \frac{1}{{\lambda }_{\min B}}=\frac{R}{4}\text{ or }{\lambda }_{\min B}=\frac{4}{R}\dots (i)\end{array}$ Similarly for Paschen series, $\begin{array}{rl}& \frac{1}{{\lambda }_{\min P}}=R\left(\frac{1}{3^2}-\frac{1}{{\infty }^2}\right)\\ & \frac{1}{{\lambda }_{\min P}}=\frac{R}{9}\text{ or }{\lambda }_{\min P}=\frac{9}{R}\dots (ii)\end{array}$ From Eqs. (i) and (ii), we get $\frac{{\lambda }_{\min \theta }}{{\lambda }_{\min P}}=\frac{4}{9}=4:9$