Physics - Modern Physics Question with Solution | TestHub

Shortest wavelength in Lyman series is given by $$\begin{array}{rl}& \frac{1}{{\lambda }_{\mathrm{I}}}=\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{\infty }\right]=\mathrm{R}\\ & \therefore {\lambda }_{\mathrm{I}}=\frac{1}{\mathrm{R}}\end{array}$$ The longest wavelength in Paschen series is given by $$\begin{array}{rl}& \frac{1}{{\lambda }_{\mathrm{p}}}=\mathrm{R}\left[\frac{1}{(3{)}^2}-\frac{1}{(4{)}^2}\right]\\ & =\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}\right]=\mathrm{R}\cdot \frac{7}{144}\\ & {\lambda }_{\mathrm{p}}=\frac{144}{7\mathrm{R}}\\ & \therefore \frac{{\lambda }_{\mathrm{p}}}{{\lambda }_{\mathrm{L}}}=\frac{144}{7}\mathrm{R}=\frac{144}{7}\\ & \therefore {\lambda }_{\mathrm{p}}=\frac{144}{7\mathrm{R}}\cdot {\lambda }_{\mathrm{L}}=\frac{144}{7}\times 912=18760\mathring{A}\end{array}$$