Physics - Modern Physics Question with Solution | TestHub

Balmer series is given for ${\mathrm{n}}_1=2$ and ${\mathrm{n}}_2=3,4,\dots$ $v=\mathrm{Rc}\left[\frac{1}{2^2}-\frac{1}{{\mathrm{n}}_2^2}\right]$ For Ist line in spectrum $n_2=3$ $\begin{array}{l}{v}_1=\mathrm{Rc}\left[\frac{1}{2^2}-\frac{1}{n_2^2}\right]=\mathrm{Rc}\left[\frac{1}{4}-\frac{1}{9}\right]=\mathrm{f}\\ \Rightarrow f=\frac{5}{36}Rc\Rightarrow Rc=\frac{36}{5}\mathrm{f}\end{array}$ For second line ${\mathrm{n}}_2=4$ $\begin{array}{rl}{v}_2=\mathrm{Rc}\left[\frac{1}{2^2}-\frac{1}{4^2}\right]& =\mathrm{Rc}\left[\frac{1}{4}-\frac{1}{16}\right]\\ & =\mathrm{Rc}\left[\frac{4-1}{16}\right]\end{array}$ $v_2=\frac{3}{16}\mathrm{Rc}=\frac{3}{16}\times \frac{36}{5}\mathrm{f}=1.35\mathrm{f}$