34 The hydrogen atom
Fig. 2.2Allowed transitions between
the configurations of hydrogen obey the
selection rule ∆l=±1. The configu-
rations withl=0, 1 , 2 , 3 , 4 ,...are la-
belleds,p,d,f,g,andsoonalphabeti-
cally (the usual convention). In the spe-
cial case of hydrogen the energy does
not depend on the quantum numberl.
−−−
lines. The series of lines to the ground configuration is called the p-
series, where p stands for principal—this is the only series observed in
absorption^40 —hence p labels configurations withl=1. Thes-seriesof(^40) ForhydrogenthisistheLymanse-
ries, as marked on Fig. 1.1; however,
p-series is a general name.
lines goes froml= 0 configurations (to a level withl= 1), and similarly
the d-series goes froml= 2 configurations; s and d stand for sharp and
diffuse, respectively.^41
(^41) These names reflect the appearance
of the lines in the first experimental ob-
servations.
2.3 Fine structure
Relativistic effects lead to small splittings of the atomic energy levels
called fine structure. We estimated the size of this structure in Section
1.4 by comparing the speed of electrons in classical orbits with the speed
of light.^42 In this section we look at how to calculate fine structure(^42) By considering elliptical orbits,
rather than just circular ones, Som-
merfeld refined Bohr’s theory to
obtain a relativistic expression for the
energy levels in hydrogen that gave
very accurate predictions of the fine
structure; however, details of that
approach are not given here.
by treating relativistic effects as a perturbation to the solutions of the
Schr ̈odinger equation. This approach requires the concept that electrons
have spin.