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

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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 $122 = \frac{\frac{1}{R}}{(\frac{1}{1^{2}} - \frac{1}{2^{2}})}$ ... (i).

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

$λ = \frac{\frac{1}{R}}{(\frac{1}{3^{2}} - \frac{1}{\infty})}$ .... (ii)

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

$λ = 823.5 nm$

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