The largest wavelength (λ1) in the ultraviolet region is the first line of the Lyman series when the electron makes a transition from n = 2 to n = 1.
1
122
= RZ2(1−
1
4
) =
3
4
RZ2 (1) The smallest wavelength in the infrared region is the last line of the Paschen series, when the electron makes a transition from n → ∞ to n = 3.