March 24, 192 1] 



NATURE 



T05 



atoms containing several electrons, due to the cir- 

 cumstance that the methods of fixing stationary 

 states were not able to remove the arbitrariness in 

 the choice of the number and configurations of the 

 electrons in the various groups, or shells, of the atom. 

 In fact, the only immediate consequence to which 

 they lead is that the motion of every electron in the 

 atom will on a first approximation correspond to one 

 of the stationary states of a system consisting of a 

 particle moving in a central field of force, which in 

 their limit are represented by the various circular or 

 elliptical stationary orbits which appear in Sommer- 

 f eld's theory of the fine structure of the hydrogen 

 lines. A way to remove the arbitrariness in question 

 is opened, however, by the introduction of the corre- 

 spondence principle, which gives expression to the 

 tendency in the quantum theory to see not merely a 

 set of formal rules for fixing the stationary states of 

 atomic systems and the frequency of the radiation 

 emitted by the transitions between these states, but 

 rather an attempt to obtain a rational generalisation 

 of the electromagnetic theory of radiation which 

 exhibits the discontinuous character necessary to 

 account for the essential stability of atoms. 



Without entering here on a detailed formulation of 

 the correspondence principle, it may be suffici^t for 

 the present purpose to say that it establishes an 

 intimate connection between the character of the 

 motion in the stationary states of an atomic system 

 and the possibility of a transition between two of 

 these states, and therefore offers a basis for a 

 theoretical examination of the process which may be 

 expected to take place during the formation and re- 

 organisation of an atom. For instance, we are led 

 by this principle directly to the conclusion that we 

 cannot expect in actual atoms configurations of the 

 type in which the electrons within each group are 

 arranged in rings or configurations of polyhedral 

 symmetry, because the form.ation of such configura- 

 tions would claim that all the electrons within each 

 group should be originally bound by the atom at the 

 same time. On the contrary, it seems necessarv to 

 seek the configurations of the electrons in the atoms 

 among such configurations as may be formed by 

 the successive binding of the electrons one by one, a 

 process the last stages of which we may assume to 

 witness in the emission of the series spectra of the 

 elements. Now on the correspondence principle we 

 are actually led to a picture of such a process which 

 not only affords a detailed insight into the structure 

 of these spectra, but also suggests a definite 

 arrangement of the electrons in the atom of a 

 type which seems suitable to interpret the high- 

 frequency spectra and the chemical properties of the 

 elements. Thus from a consideration of the possible 

 transitions between stationary states, corresponding 

 to the various steps of the binding of each of the 

 electrons, \ye are led in the first place to assume that 

 onlv the two first electrons move in what may be 

 called one-quantum orbits, which are analogous to 

 that stationary state of a central system which corre- 

 sponds to the normal state of a system consisting of 

 one electron rotating round a nucleus. The electrons 

 bound after the first two will not be able by a transi- 

 tion between two stationary states to procure a posi- 

 tion in the atom equivalent to that of these two 

 electrons, but will move in what may be called 

 multiple-quanta orbits, which correspond to other 

 stationary state?? of a central system. 



The assumption of the presence in the normal state 

 of the atom of such multiple-quanta orbits has already 

 been introduced in various recent theories, as, for 

 instance, in Sommerfeld's work on the high-frequency 

 spectra and in that of Land^ on atomic dimen- 



NO. 2682, VOL. 107] 



sions and crystal structure; but the application of the 

 correspondence principle seems to otter for the first 

 time a rational theoretical basis for these conclusions 

 and for the discussion of the arrangement of the orbits 

 of the electrons bound after the first two. Thus by 

 means of a closer examination of the progress of the 

 binding process this principle offers a simple argu- 

 ment for concluding that these electrons are arranged 

 in groups in a way which reflects the periods 

 exhibited by the chemical properties of the elements 

 within the sequence of increasing atomic numbers. 

 In fact, if we consider the binding of a large number 

 of electrons by a nucleus of high positive charge, 

 this argument suo'^ests that after the first two elec- 

 trons are bound in one-quantum orbits, the next eight 

 electrons will be bound in two-quanta orbits, the next 

 eighteen in three-quanta orbits, and the next thirty- 

 two in four-quanta orbits. 



Although the arrangements of the orbits of the 

 electrons within these groups will exhibit a remark- 

 able degree of spatial symmetry, the groups cannot 

 be said to form simple shells in the sense in 

 which this expression is generally used as regards 

 atomic constitution. In the first place, the argument 

 involves that the electrons within each group do not 

 all play equivalent parts, but are divided into sub- 

 groups corresponding to the different types of 

 multiple-quanta orbits of the same total number of 

 quanta, which represents the various stationary states 

 of an electron moving in a central field. Thus, cor- 

 responding to the fact that in such a system there 

 exist two types of two-quanta orbits, three types of 

 three-quanta orbits, and so on, we are led to the view 

 that the above-mentioned group of eight electrons 

 consists of two sub-groups of four electrons each, 

 the group of eighteen electrons of three sub-groups 

 of six electrons each, and the group of thirty-two 

 electrons of four sub-groups of eight electrons each. 



Another essential feature of the constitution 

 described lies in the configuration of the orbits of 

 the electrons in the different groups relative to each 

 other. Thus for each group the electrons within 

 certain sub-groups will penetrate during their revolu- 

 tion into regions which are closer to the nucleus 

 than the mean distances of the electrons belonging 

 to groups of fewer-quanta orbits. This circumstance, 

 which is intimately connected with the essential 

 features of the processes of successive binding, gives 

 just that expression for the "coupling" between the 

 different groups which is a necessary condition for 

 the stability of atomic configurations. In fact, this 

 coupling is the predominant feature of the whole 

 picture, and is to be taken as a guide for the inter- 

 pretation of all details as regards the formation of 

 the different groups and their various sub-groups. 

 Further, the stability of the whole configuration is 

 of such a character that if any one of the electrons 

 is removed from the atom by external agencies not 

 only may the previous configuration be reorganised bv 

 a successive displacement of the electrons within the 

 sequence in which they were originally bound by the 

 atom, but also the place of the removed electron may 

 be taken by any one of the electrons belonging to more 

 loosely bound groups or sub-groups through a process 

 of direct transition between two stationary states, ac 

 companied by an emission of a monochromatic radia- 

 tion. This circumstancp — which offers a basis for a 

 detailed interpretation of the characteristic structure 

 of the high-frequency spectra of the elements — is inti- 

 mately connected with the fact that the electrons in 

 the various sub-groups, although they may be said 

 to play equivalent parts in the harmony of the inter- 

 atomic motions, are not at every moment arranged 

 in configurations of simple axial or polyhedral sym~ 



