Calculate the wavelength of the second line of Lyman series in a spectrum of hydrogen atom. (Take Rydberg constant, $\displaystyle \mathrm{R}=1 \cdot 1 \times 10^{7} \mathrm{~m}^{-1}$ )

\(\displaystyle \frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_{1}{ }^{2}}-\frac{1}{\mathrm{n}_{2}{ }^{2}}\right]\) For second line of Lyman series \(\displaystyle \mathrm{n}_{1}=1, \mathrm{n}_{2}=3\) \(\displaystyle \frac{1}{\lambda}=1.1 \times 10^{7}\left[\frac{1}{1^{2}}-\frac{1}{3^{2}}\right]\) \(\displaystyle =1.1 \times 10^{7}\left[1-\frac{1}{9}\right]\) \(\displaystyle =1.1 \times 10^{7} \times \frac{8}{9}\)