What is the shortest wavelength line spectrum (in nanometers) in the Lyman series of the hydrogen atomic spectrum? $\left(\mathrm{R}=1.096\times {10}^7{\mathrm{m}}^{-1}\right)$

$\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}\left|\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right|$
The shortest wave length line occurs when  ${\mathrm{\eta }}_2=\mathrm{\infty }$
So that $\frac{1}{{\mathrm{n}}_2^2}$is zero    $\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}\left|\frac{1}{1^2}-\frac{1}{{\mathrm{\infty }}^2}\right|$
$\begin{array}{l}=1.096\times {10}^{-2}{\mathrm{nm}}^{-1}(1-0)=1.096\times {10}^{-2}{\mathrm{nm}}^{-1}\\ \mathrm{\lambda }=\frac{1}{1.096\times {10}^{-2}{\mathrm{nm}}^{-1}}=91.24\mathrm{nm}\end{array}$
The shortest wavelength line in the Lyman series is 91.24nm