The shortest wavelength in Lyman series is 91.2 nm . The longest...

The wavelength ($\lambda )$ of lines is given by

$\dfrac{1}{\lambda} = R \left(\dfrac{1}{{1}^{2}} - \dfrac{1}{n^{2}}\right)<br /><br />For Lyman series, the shortest wavelength is for$ n$=\infty$ and longest is for n = 2$.<br /><br />$∴ $\dfrac{1}{{\lambda}_{s}} =$ R\left(\dfrac{1}{{1}^{2}}\right) \ldots ($i )$

\dfrac{1}{{\lambda}_{L}} =$R\left(\dfrac{1}{1} - \dfrac{1}{{2}^{2}}\right) = \dfrac{3}{4}$ R$...(ii)<br /><br />Dividing Eq.(ii) by Eq. (i) , we get<br /><br />\dfrac{{\lambda}_{L}}{{\lambda}_{s}} = \dfrac{4}{3}<br /><br />Given,${\lambda}_{s} = 91.2 $\text{nm}<br /><br />$⇒ {\lambda}_{L}$= 91.2 \times \dfrac{4}{3} =121.6 \text{nm}$