The series in UV region is Lyman series. Longest wavelength corresponds to minimum energy which occurs in the transition from n = 2 to n = 1.

Therefore $122=\genfrac{}{}{0.1ex}{}{\genfrac{}{}{0.1ex}{}{1}{R}}{(\genfrac{}{}{0.1ex}{}{1}{1^2}-\genfrac{}{}{0.1ex}{}{1}{2^2})}$ ... (i).

The smallest wavelength in the infrared region corresponds to a maximum energy of the Paschen series.

$\lambda =\frac{\frac{1}{\text{R}}}{\left(\frac{1}{3^2}-\frac{1}{\infty }\right)}$ .... (ii)

Solving Eqs. (i) and (ii), we get

$\mathrm{\lambda } = 823.5 \mathrm{nm}$