The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is _______nm

For smallest frequency and largest wavelength in U.V region. Electron transition form orbit 2 to orbit 1

$\begin{array}{l}\frac{1}{\lambda }=R\left[\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}\right]\\ \frac{1}{122}=R\left[\frac{1}{{\left(1\right)}^2}-\frac{1}{{\left(2\right)}^2}\right]\\ \frac{1}{122}=\frac{3R}{4}\\ R=\frac{4}{3\times 122}-----\left(1\right)\end{array}$

For highest frequency and smallest wave length in  I. R Region i.e., $n_1=3,n_2=\alpha$

$\begin{array}{l}\frac{1}{\lambda }=R\left[\frac{1}{\left(3\right)}-\frac{1}{{\left(\infty \right)}^2}\right]\\ \frac{1}{\lambda }=\frac{4}{3\times 122}\times \frac{1}{9}\\ \lambda =\frac{366\times 9}{4}\\ \lambda =823nm\end{array}$