The Balmer equation for the wavelengths of the hydrogen lines is
| (1) |
which derives from the energy of each level, En = const n2.
The various lines of hydrogen are grouped together according to their lowest level. All transitions involving the ground level, n=1, are called Lyman lines. All those with n=2 as lowest level are called Balmer lines, and those down to or up from n=3 are called Paschen lines.
Within each group of lines, the lines are ordered according to Dn. Each transition involving a change in n of 1 is called an a transition; D = 2 is a b transition, and so on. An electron in level n=3, going down to n=1, has the choice of either two successive a transitions, or one b.
Each transition is indicated by its family name and Dn. The transition from n=2 ®1 is called a Lya line; n=3®1 becomes a Lyb line. The full set of these lines are called the Lyman series. Similarly, the Balmer series are ordered as Ha, Hb, Hg, etc. (For historical reasons, they are indicated by 'H' even though they are called Balmer lines). The Paschen series is written as Paa, etc.
In the example above, the electron going from n=3 to n=1 can either cause an Ha photon and a Lya photon, or one Lyb photon.
The Lyman, Balmer and Paschen series are well separated in wavelength. All Lyman lines are in the ultraviolet. The Balmer lines are in the optical, and the Paschen lines are infrared lines.
A figure of the hydrogen spectrum shows how the lines are grouped.
(Source: www.physics.udel.edu/~watson/ALLSTEL99/img004.GIF)