Two distinct problems are involved. First, the specification of the orbits of all the electrons in an atom in the normal state and in the states which are most probable when the atom is excited. Secondly, the determination of the spectroscopic terms corresponding to these various states. The former problem has been solved mainly through the labours of Bohr, Main Smith and Stoner; the results so far as the normal state are concerned will be found elsewhere. (See ATOM, MAGNETISM, QUANTUM THEORY.) The same results for the arrangement of electrons in the normal atoms of the elements also follow from Pauli's exclusion principle, which asserts that not more than one electron can have the same four quantum numbers which are now necessary to define its motions completely. Thus, proceeding outwards from the nucleus, the so-called K shell, or group, cannot contain more than two electrons, the L shell eight, and so on. In excited states the outermost, or valence, electrons are most easily disturbed and experience has shown that their movements usually account for the most prominent terms occurring in spectra.
The solution of the second problem is largely due to the work of Heisenberg and Hund, the whole theory being based on the supposition that the angular momenta of all the rotary motions within the atom can only be changed by unit steps. These rotary motions, for each individual electron, require four quantum num bers for their complete specification. Besides n and k, which deter mine the size and shape of the orbit, there are also two so-called "magnetic quantum numbers," one of them involving the orienta tion of the orbit and the other the direction of spin, each electron being assigned half a unit of angular momentum. The problem of predicting the spectroscopic terms for different arrangements of the electrons is, fortunately, greatly simplified by the fact that electrons which are in completely filled groups can be disre garded, as it follows from Pauli's principle that the resultant angular momentum for such groups is zero. The general outcome of the extended theory is that the quantum numbers which define the spectroscopic terms are now to be regarded as resultants of those which define the characteristics of the outer or valence electrons. The process by which the terms are deduced from the atomic states, however, is too complex to be described here, and, in fact can scarcely be indicated completely in terms of the orbital model of the atom.
The theoretical prediction of the spectroscopic terms to be expected for given configurations of the electrons, however, has already been of immense service in the disentanglement of many complicated spectra, and there is every reason to believe that the elucidation of the structures of all line spectra, and their corre lation with atomic structures, is not far distant.
Spectroscopy. E. C. C. Baly (Longmans, London) 3 vols. published 1924-27 ; 4th and final volume in preparation. A general survey for serious students.
The Spectroscope and its Work. H. F. Newall (Soc. for Promoting Christian Knowledge, London, 1910). A small semi-popular book giving a good introduction to the subject, including astrophysical applications.
Spectroscopy of the Extreme Ultra-Violet. T. Lyman (Longmans, London, 1928). A full account of work with the vacuum spectrograph. Lines in the Arc Spectra of the Elements. F. Stanley (Adam Hilger, London, 1911). A useful list of the principal lines in arc spectra, arranged in order of wave-lengths, from 2 200 to 7950A.
Wave-Length Tables for Spectrum Analysis. F. Twyman (Adam Hilger, London, 1923). Includes standard wave-lengths from 2375A to 8495A, and the most persistent lines of the majority of the elements.
See further the Bibliography to ATOM, for books discussing the bear ing of the modern theory of the atom on spectroscopy.
Visual Lines for Spectrum Analysis. D. M. Smith (Adam Hilger, London, 1928). A short and simple guide to practical spectrum analysis.
Report on Series in Line Spectra. A. Fowler (Fleetway Press, Lon don, 1922). Gives an account of the analysis of spectra to 1922, with many useful tables.
Atomic Structure and Spectral Lines. A. Sommerfeld, English trans lation of 3rd German edition (Methuen, London, 1923) 4th German edition (Vieweg, Braunschweig, 1924). An extended account of the theory of spectra to date of publication.
Linienspektren and Periodisches System der Elemente. F. Hund (Julius Springer, Berlin, 1927). A small but important book, explain ing the correlation of spectral and atomic structures. (A. Fow.)