7 - Understanding atomic spectra – additional quantum numbers

Summary

Optical spectroscopy, multiplets and the splitting of spectral lines

The achievements described in Chap. 6 represented a remarkable advance in the understanding of quantum phenomena, but there remained major challenges which were ultimately to undermine the successes of the old quantum theory. Continuing advances in spectroscopy enabled high resolution spectra to be obtained and, with the ability to place the sources of emission in strong electric and magnetic fields, the full complexity of atomic and molecular spectra became apparent. Atomic spectra display regularities, for example, the series spectra of elements such as sodium and calcium which could be described by the Rydberg formula (Sect. 1.6). Some of the most prominent spectral features consisted, however, of multiplets, meaning the splitting of a line into a number of separate lines with similar wavelengths. Examples of multiplets are illustrated in Fig. 7.1, derived from observations of the photosphere of the Sun from the Pic du Midi observatory.

The simplest lines are singlets, the example of the Hα line of the Balmer series of hydrogen being shown in Fig. 7.1a. In fact, the line is a very narrow doublet, which Sommerfeld attributed to the effects of special relativity upon the circular and elliptical orbits of electrons of the same principal quantum number (Sect. 5.3). The splittings we are interested in here are very much larger effects. The classic example of a doublet is the splitting of the sodium D line into two bright components labelled D₁ (589.592 nm) and D₂ (588.995 nm) (Fig. 7.1b).