40 



Supplement to '* Nature^' July 7, 1923 



electron orbits. Indeed, it was possible, with the aid 

 of the correspondence principle, to account completely 

 for the characteristic rules which govern the seemingly 

 capricious occurrence of combination lines, and it is 

 not too much to say that the quantum theory has 

 not only provided a simple interpretation of the 

 combination principle, but has further contributed 

 materially to the clearing up of the mystery that 

 has long rested over the application of this principle. 



The same view-points have also proved fruitful in 

 the investigation of the so-called band spectra. These 

 do not originate, as do series spectra, from individual 

 atoms, but from molecules ; and the fact that these 



Fig. 8. 



spectra are so rich in lines is due to the complexity 

 of the motion entailed by the vibrations of the atomic 

 nuclei relative to each other and the rotations of 

 the molecule as a whole. The first to apply the 

 postulates to this problem was Schwarzschild, but 

 the important work of Heurlinger especially has 

 thrown much light on the origin and structure of 

 band spectra. The considerations employed here can 

 be traced back directly to those discussed at the 

 beginning of this lecture in connexion with Bjerrum's 

 theory' of the influence of molecular rotation on the 

 infra-red absorption lines of gases. It is true we no 

 longer think that the rotation is reflected in the spectra 

 in the way claimed by classical electrodynamics, but 

 rather that the line components are due to transitions 

 between stationary states which differ as regards 

 rotational motion. That the phenomenon retains 

 its essential features, however, is a typical consequence 

 of the correspondence principle. 



The Natural System of the Elements. 



The ideas of the origin of spectra outlined in the 

 preceding have furnished the basis for a theory of the 

 structure of the atoms of the elements which has 

 shown itself suitable for a general interpretation of 

 the main features of the properties of the elements, 

 as exhibited in the natural system. This theory is 

 based primarily on considerations of the manner in 

 which the atom can be imagined to be built up by the 

 capture and binding of electrons to the nucleus, one 



by one. As we have seen, the optical spectra of 

 elements provide us with evidence on the progress 

 of the last steps in this building up process. 



An insight into the kind of information that the 

 closer investigation of the spectra has provided in this 

 respect may be obtained from Fig. 8, which gives a 

 diagrammatic representation of the orbital motion in 

 the stationary states corresponding to the emission 

 of the arc-spectrum of potassium. The curves show 

 the form of the orbits described in the stationary 

 states by the last electron captured in the potassium 

 atom, and they can be considered as stages in the 

 process whereby the 19th electron is bound after the 

 18 previous electrons have already 

 been bound in their normal orbits. 

 In order not to complicate the 

 figure, no attempt has been made 

 to draw any of the orbits of these 

 inner electrons, but the region in 

 which they move is enclosed by 

 a dotted circle. In an atom with 

 several electrons the orbits will, 

 in general, have a complicated 

 character. Because of the sym- 

 metrical nature of the field of force 

 about the nucleus, however, the 

 motion of each single electron can 

 be approximately described as a 

 plane periodic motion on which is 

 superimposed a uniform rotation in 

 the plane of the orbit. The orbit 

 of each electron will therefore be to a 

 first approximation doubly periodic, 

 and will be fixed* by two quantum 

 numbers, as are the stationary states in a hydrogen atom 

 when the relativity precession is taken into account. 



In Fig. 8, as in Fig. 5, the electron orbits are marked 

 with the symbol w^, where n is the principal quantum 

 number and h the subordinate quantum number. 

 While for the initial states of the binding process, 

 where the quantum numbers are large, the orbit of 

 the last electron captured lies completely outside of 

 those of the previously bound electrons, this is not 

 the case for the last stages. Thus, in the potassium 

 atom, the electron orbits with subordinate quantum 

 numbers 2 and i will, as indicated in the figure, 

 penetrate partly into the inner region. Because of 

 this circumstance, the orbits will deviate very greatly 

 from a simple Kepler motion, since they will consist 

 of a series of successive outer loops that have the 

 same size and form, but each of which is turned through 

 an appreciable angle relative to the preceding one. 

 Of these outer loops only one is shown in the figure. 

 Each of them coincides very nearly with a piece of 

 a Kepler ellipse, and they are connected, as indicated, 

 by a series of inner loops of a complicated character 

 in which the electron approaches the nucleus closely. 

 This holds especially for the orbit with subordinate 

 quantum number i, which, as a closer investigation 

 shows, will approach nearer to the nucleus than any 

 of the previously bound electrons. 



On account of this penetration into the inner region, 

 the strength with which an electron in such an orbit 

 is bound to the atom will — in spite of the fact that 

 for the most part it moves in a field of force of the 



