What are the wavelengths of two …

According to Rydberg Balmer equation
{tex}\frac{1}{\lambda}{/tex} = {tex}R\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]=R\left[\frac{1}{1^{2}}-\frac{1}{n_{2}^{2}}\right]{/tex}
The wavelength {tex}(\lambda){/tex}will be longest when n₂ is the smallest i.e. n = 2 and 3 for two longest wavelength lines.
For : n₂ = 2 , {tex}\frac{1}{\lambda}=\left(1.097 \times 10^{-2} \mathrm{nm}^{-1}\right)\left[\frac{1}{1^{2}}-\frac{1}{2^{2}}\right]{/tex}
{tex}\left(1.097 \times 10^{-2} \mathrm{nm}^{-1}\right) \times \frac{3}{4}=8.228 \times 10^{-3} \mathrm{nm}^{-1}{/tex} or {tex}\lambda=121.54 \mathrm{nm}{/tex}
For: n₂ = 3; {tex}\frac{1}{\lambda}=\left(1.097 \times 10^{-2} \mathrm{nm}^{-1}\right){/tex}
= {tex}\left(1.097 \times 10^{-2} \mathrm{nm}^{-1}\right) \times(8 / 9)=9.75 \times 10^{-3} \mathrm{nm}^{-1}{/tex}; {tex}\lambda=102.56 \mathrm{nm}{/tex}