In Hydrogen spectrum the shortest wavelength in Balmer series is $\mathrm{\lambda }$ . The shortest wavelength in the Brackett series will be

For shortest wavelength in Balmer series, ${\mathrm{n}}_1=2,{\mathrm{n}}_2=\infty$

$\frac{1}{\mathrm{\lambda }}=\mathrm{R}\left(\frac{1}{4^2}-\frac{1}{\infty }\right)\Rightarrow \mathrm{\lambda }=\frac{4}{\mathrm{R}}$

For shortest wavelength in Brackett series, ${\mathrm{n}}_1=4,{\mathrm{n}}_2=\infty$

$\therefore \frac{1}{\mathrm{\lambda }\text{'}}=\mathrm{R}\left(\frac{1}{4^2}-\frac{1}{\infty }\right)\Rightarrow \mathrm{\lambda }\text{'}=\frac{16}{\mathrm{R}}=4\mathrm{\lambda }$