42 



Supplement to '' Nature y'July 7, 1923 



processes of the electrons in the atom, of which we 

 have experimental evidence in optical spectra, and 

 the characteristic features of which have been elucidated 

 principally by the correspondence principle. It is 

 here an essential circumstance that the restriction on 

 the course of the binding process, which is expressed 

 by the presence of electron orbits with higher 

 quantum numbers in the normal state of the atom, 

 can be naturally connected with the general condition 

 for the occurrtnce of transitions between stationary 

 states, formulated in that principle. 



Another essential feature of the theory is the 

 influence, on the strength of binding and the dimensions 

 of the orbits, of the penetration of the later bound 

 electrons into the region of the earlier bound ones, 

 of which we have seen an example in the discussion 

 of the origin of the potassium spectrum. Indeed, this 

 circumstance may be regarded as the essential cause 

 of the pronounced periodicity in the properties of 

 the elements, in that it implies that the atomic dimen- 

 sions and chemical properties of homologous substances 

 in the differfent periods, as, for example, the alkali- 

 metals, show a much greater similarity than that 

 which might be expected from a direct comparison 

 of the orbit of the last electron bound with an 

 orbit of the same quantum number in the hydrogen 

 atom. 



The increase of the principal quantum number 

 which we meet when we proceed in the series of the 

 elements, affords also an immediate explanation of 

 the characteristic deviations from simple periodicity 

 which are exhibited by the natural system and are 

 expressed in Fig. i by the bracketing of certain series 

 of elements in the later periods. The first time such 

 a deviation is met with is in the 4th period, and the 

 reason for it can be simply illustrated by means of 

 our figure of the orbits of the last electron bound in 

 the atom of potassium, which is the first element in 

 this period. Indeed, in potassium we encounter for 

 the first time in the sequence of the elements a case 

 in which the principal quantum number of the orbit 

 of the last electron bound is, in the normal state of 

 the atom, larger than in one of the earlier stages of 

 the binding process. The normal state corresponds 

 here to a % orbit, which, because of the penetration 

 into the inner region, corresponds to a much stronger 

 binding of the electron than a 4-quantum orbit in 

 the hydrogen atom. The binding in question is 

 indeed even stronger than for a 2-quantum orbit 

 in the hydrogen atom, and is therefore more than 

 twice as strong as in the circular 33 orbit which is 

 situated completely outside the inner region, and for 

 which the strength of the binding differs but little 

 from that for a 3-quantum orbit in hydrogen. 



This will not continue to be true, however, when 

 we consider the binding of the 19th electron in sub- 

 stances of higher atomic number, because of the much 

 smaller relative difference between the field of force 

 outside and inside the region of the first eighteen 

 electrons bound. As is shown by the investigation 

 of the spark spectrum of calcium, the binding of the 

 19th electron in the 4i orbit is here but little stronger 

 than in 33 orbits, and as soon as we reach scandium, 

 we must assume that the 33 orbit will represent the 

 orbit of the 19th electron in the normal state, since 



this type of orbit will correspond to a stronger binding 

 than a 4i orbit. While the group of electrons in 

 2-quantum orbits has been entirely completed at the 

 end of the 2nd period, the development that the group 

 of 3-quantum orbits undergoes in the course of the 

 3rd period can therefore only be described as a pro- 

 visional completion, and, as shown in the table, this 

 electron group will, in the bracketed elements of the 

 4th period, undergo a stage of further development 

 in which electrons are added to it in 3-quantum orbits. 



This development brings in new features, in that 

 the development of the electron group with 4-quantum 

 orbits comes to a standstill, so to speak, until the 

 3-quantum group has reached its final closed form. 

 Although we are not yet in a position to account in 

 all details for the steps in the gradual development 

 of the 3-quantum electron group, still we can say that 

 with the help of the quantum theory we see at once 

 why it is in the 4th period of the system of the elements 

 that there occur for the first time successive elements 

 with properties that resemble each other as much 

 as the properties of the iron group ; indeed, we can 

 even understand why these elements show their well- 

 known paramagnetic properties. Without further 

 reference to the quantum theory, Ladenburg had on 

 a previous occasion already suggested the idea of 

 relating the chemical and magnetic properties of these 

 elements with the development of an inner electron 

 group in the atom. 



I will not enter into many more details, but only 

 mention that the peculiarities we meet with in the 

 5th period are explained in much the same way as 

 those in the 4th period. Thus the properties of the 

 bracketed elements in the 5th period as it appears 

 in the table, depend on a stage in the development 

 of the 4-quantum electron group that is initiated by 

 the entrance in the normal state of electrons in 43 orbits. 

 In the 6th period, however, we meet new features. 

 In this period we encounter not only a stage of the 

 development of the electron groups with 5- and 

 6-quantum orbits, but also the final completion of 

 the development of the 4-quantum electron group, 

 which is initiated by the entrance for the first time 

 of electron orbits of the 44 type in the normal state 

 of the atom. This development finds its characteristic 

 expression in the occurrence of the peculiar family 

 of elements in the 6th period, known as the rare-earths. 

 These show, as we know, a still greater mutual similarity 

 in their chemical properties than the elements of the 

 iron family. This must be ascribed to the fact that 

 we have here to do with the development of an electron 

 group that lies deeper in the atom. It is of interest 

 to note that the theor>^ can also naturally account 

 for the fact that these elements, which resemble 

 each other in so many ways, still show great differences 

 in their magnetic properties. 



The idea that the occurrence of the rare-earths 

 depends on the development of an inner electron 

 group has been put forward from different sides. 

 Thus it is found in the work of Vegard, and at the 

 same time as my own work, it was proposed by Bury 

 in connexion with considerations of the systematic 

 relation between the chemical properties and the 

 grouping of the electrons inside the atom from the 

 point of view of Langmuir's static atomic model. While 



