ATOMIC CONSTITUTION AND THE PERIODIC TABLE Soon after the discovery of the electron it was recognized that the relationships between the physical and chemical properties of the elements expressed in the periodic table point towards a group-structure of the electronic distribution in the atom. Fun damental work on these lines was done by J. J. Thomson in After the discovery of the nucleus and the simple interpretation of the atomic number given above, his work has been followed up with great success especially by Kossel and Lewis.
It is suggested that the electrons within the atom possess a tendency to f orm stable groups, each containing a definite number of electrons which, in the neutral state of the atom, surround the centre of the atom like successive shells or layers. An explanation of the simple valency properties holding for the second and third period of the periodic table was, for instance, obtained by assum ing that there was a tendency to form completed shells each con taining eight electrons. The single valency of sodium and the double valency of magnesium are ascribed to the facility with which the neutral atoms of these elements can lose one or two electrons respectively, as the atomic ions remaining would then contain completed shells only. On the other hand the double negative valency of sulphur and the single negative valency of chlorine are ascribed to the tendency of their outermost shells to take up two or one additional electrons respectively in order to form a complete shell of eight electrons, like that contained in the neutral atom of the inactive gas argon.
To each step there corresponds a multitude of stages, i.e., stationary states, in which the electron is more and more firmly bound to the atom. The final state, in which binding is strongest, corresponds to the normal state of the atomic ion. A definite connection between the spectra and the group structure was now established by assuming that, in the normal atom only a limited number of electrons can be bound in states visualized as orbits characterized by definite values of the quantum numbers n and k. The electrons bound in orbits corresponding to a given value of n are said to form an n-quantum group, which in its finally com pleted stage will contain n subgroups, corresponding to the possi ble values I, 2 . . . n which k may take. For a sufficiently large nuclear charge, the strength with which the electrons in the different subgroups belonging to one and the same group are bound will be nearly equal.
In the gradual building up of the groups in atoms with increas ing nuclear charge, it is, however, to be noted that when an orbit appears for the first time in the neutral atom, the strength of the binding will depend very considerably on the value of k. This is due to the circumstance that this quantum number fixes the closest distance to which the electron may approach the nucleus. The screening of the nuclear charge by the other elec trons in the atom may therefore be very different for orbits cor responding to different values of k, and the effect on the strength of the binding can be so large that an orbit characterized by cer tain values of n and k may correspond to a stronger binding than an orbit for which n is smaller but k larger. This offers a natural explanation of one feature of the periodic table, namely that the periods grow gradually larger, while there appear sequences of elements which differ comparatively little in their chemical and physical properties. Such a sequence marks a stage in the de velopment of an n-quantum group, which consists in the addition of a subgroup corresponding to a value of k which was previously not yet represented in that group, and which takes place after the building up of a group corresponding to a higher value of is has already begun. In fact, during the addition of the subgroup a temporary standstill will occur in the development of the latter group, the constitution of which will primarily determine the chemical affinity of the atom, since it contains the most loosely bound electrons.
In the accompanying table (Table II.) is given a summary of the structure of the normal state of the neutral atoms of the elements. The figures before the different elements are the atomic numbers, which give the total number of electrons in the neutral atom. The figures in the different columns give number of electrons in orbits corresponding to values of the principal and subordinate quantum numbers standing at the top. A comparison with the periodic table (Table I.) will show that those elements which in chemical respect are homologous, will have the same number of electrons in the electronic groups most loosely bound, containing the so-called valence-electrons. The atoms of elements which in Table I. are enclosed in brackets possess electronic configurations in which a subgroup is being added to a group, whose principal number is less than the group containing the typical valence electrons. An especially conspicuous example of such a completion of an inner group is offered by the elements forming the family of the rare earths. Here we witness the addition of the fourth sub group to the 4-quantum group, which begins first in Ce (58) while the addition of the third subgroup was already finished in Ag (47).
Table II. is in general agreement not only with the optical spectral evidence but also with that in the region of X-rays. As mentioned earlier, we see in X-ray spectra a change in the binding of an electron in the interior of the atom. This takes place when, for instance, by the impact of a swiftly moving particle on the atom, an electron is removed from one of the electronic groups, and its place is taken by an electron belonging to a group for which the binding energy is smaller. As an example it may be stated that the strong X-ray whose frequency is approximately represented by formula (4) is emitted when an electron has been removed from the i -quantum group, and one of the electrons performs a transition so as to occupy the empty place. The line represented approximately by formula (5) originates from a transition by which a 3, electron takes the place left open upon the removal of a 2, electron.
The question how many electrons there are in the various groups and subgroups has been subject to much discussion in the last few years. Table II. is the temporary result of this discussion and seems to give an adequate description of the spectral as well as the chemical evidence. It is clear that a full theoretical treat ment of the problem cannot be obtained from considerations based only on the simple picture of central orbits. Such a treatment will essentially involve an examination of those features of the binding of the electrons, which appear in the multiplet structure of spectral lines. Indeed it is very probable that the idea that the electron itself has magnetic properties may give the clue to the interpretation of the empirical rules governing the number of electrons in the group structure of the atom.
Recent Progress.—Such is the outline of the theory of the atom and its structure as it stood in 1925. Since then the subject of atomic structure has undergone a remarkable development due to the establishment of rational quantum theoretical methods which enable a quantitative treatment to be given to a large number of atomic problems that, earlier, were accessible only to considerations of a more qualitative character. These methods take their origin from two sources. On the one hand the symbolic procedure of "quantum mechanics" initiated by Heisenberg, and briefly referred to above, has, thanks to the collaboration of a num ber of eminent physicists, developed into a structure which, as re gards generality and consistency, may be compared with the theory of classical mechanics. On the other hand a new method of "wave mechanics" of great power and fertility has been de veloped by Schrodinger having its starting point in the pioneer work of de Broglie. (See QUANTUM THEORY.) This method utilizes the analogy between mechanics and optics emphasized already long ago by Hamilton. According to de Broglie, the mo tion of a material particle may be compared with the propaga tion of a train of waves, the frequency of which is related to the kinetic energy of the particle, as calculated on the relativity theory, by the general quantum relation E=hv. Indeed, this view may be considered as an inversion of the considerations by which Einstein was led to the hypothesis that the carrier of light energy had to be considered not as waves but as corpuscles—the so called light quanta—which concentrated within a small volume contained the energy hv. Notwithstanding the indispensability of the wave theory of light for the account of ordinary optical expe rience, Einstein's hypothesis has proved most fruitful in explain ing a number of phenomena, notably the important discovery of Compton of the change in the frequency which X-rays suffer when scattered by electrons. Similarly the view of de Broglie, strange as it is from the classical point of view, has received a striking support from the recent discovery of Davisson and ter mer about the selective reflection of electrons from metal crystals. Indeed, in these experiments the electrons were found to behave as waves possessing the wave length anticipated from quantum theory.
The first indication of the importance of the wave idea in the problem of atomic constitution was the suggestion of de Broglie that the stationary states of an atom might be interpreted as an interference effect of the waves associated with a bound electron. A real advance in this .direction, however, was first achieved by Schrodinger, who succeeded in replacing the classical equations of motion for the particles in the atom by a certain differential equation of a type similar to that known from the theory of elastic vibrations of solid bodies. As is well known from acous tics any such vibration can be resolved into a number of purely harmonic components, representing the fundamental tones of a musical instrument. It was now found that the "characteristic solutions" of the Schrodinger wave equation, corresponding to such purely harmonic vibrations, offer a detailed interpretation of the properties of stationary states. First of all the energy values appearing in the quantum theory of spectra are obtained by multiplying the frequencies of the characteristic vibrations by Planck's constant. Next Schrodinger succeeded in associating with the solution of his wave equation a continuous distribution of electric charge and current, which, when applied to a charac teristic vibration, represents the electrostatic and magnetic prop erties of an atom in the corresponding stationary state. Simi larly the superposition of two characteristic solutions corresponds to a continuous vibrating distribution of electric charge, which on classical electrodynamics would give rise to an emission of radia tion, fulfilling the requirement of the quantum postulate and the correspondence principle as regards frequency as well as intensity and polarization.
These remarkable results have given rise to a renewed dis cussion regarding the physical nature of the constituents of the atom. Indeed, the view has been advocated that the wave idea offers a real picture of the atom, allowing a direct application of the methods of classical physics. On this view the wave mechanics represent a natural generalization of classical mechanics of ma terial particles, to which it is related in the same way as the modern theory of optics based on the fundamental equations of electrodynamics is related to the more primitive theory of geo metrical optics, which makes use of the idea of light rays. It would appear, however, that the situation is more complicated. Due to the very contrast between the ideas of quantum theory and the fundamental principles of classical physics, we cannot expect to be able to visualize atomic phenomena by means of our classi cal ideas. In the dilemma regarding the nature of light and the ultimate constituents of matter we witness a general feature of a dualism inherent in the quantum theory description. Indeed, the wave and particle ideas are both indispensable if we attempt to get a full description of experience. This situation is brought out very clearly by the recent development of the symbolic method of quantum mechanics, through which an intimate connection be tween the correspondence argument and Schrodinger's work is established. Just when due regard is given to the feature of dualism in question, the quantum theory can, unfamiliar as it is, still be regarded as a natural development of the ordinary descrip tion of physical phenomena.
In the problem of atomic constitution we meet with a very striking example of the dualism mentioned. Notwithstanding the wonderful power of the Schrodinger wave functions of illustrating properties of stationary states, the wave theory fails to account for the peculiar stability of these states, on which the interpreta tion of atomic phenomena rests so essentially. Indeed, we have here to do with the very feature of discontinuity or rather "in dividuality," by which the quantum theory departs from the ideas of classical physics, and of which we perhaps have the most striking example in the existence of the individual particles themselves. For the rest, the dualism of the quantum theory brings with it the conclusion that the use of the idea of station ary states excludes the possibility of following at the same time the behaviour of the single particles in the atom. Just this situa tion finds its adequate representation in the characteristic vibra tions of the Schrodinger wave problem. This problem, in fact, is not a 3-dimensional one, as that of ordinary spatial description, but one which operates with a number of dimensions equal to the num ber of degrees of freedom of the whole atom. This fact has re cently found an important application in the interpretation of a certain peculiar duplexity in the structure of spectra especially marked in the helium spectrum. This duplexity, which for a long time eluded explanation, has recently been explained by Heisen berg, who pointed out that we have here to do with an effect of the mutual interaction of the electrons in the atom, which exhib its a close correspondence with a classical resonance problem, but cannot be accounted for on the simple procedure of characterizing the behaviour of the individual electrons by quantum numbers. The justification of this procedure in a large number of applica tions rests on the circumstance that in general the resonance effect is very small, the mutual influence of the various electrons on each other being, as already described, to a close approximation to that of a conservative central field of force.
It is impossible here to give anything but a vague idea of the abundance of details regarding the physical and chemical proper ties of the elements which have been explained by means of the new methods of quantum theory. It may still be mentioned that the important contributions of Main Smith and Stoner to the in terpretation of the periodic table—embodied already in the scheme of electron orbits given in the article—have been brought into most convincing connection with the so-called exclusion principle of Pauli and with the idea of the magnetic electron re ferred to already. Moreover a study of the fine structure of band spectra has led to the conclusion that the proton, or the nucleus of the hydrogen atom, also possesses an angular mo mentum and a magnetic moment. Quite recently even a suc cessful attack on the fundamental problem of the origin of the so-called electron spin has been made by Dirac, whose work has opened new prospects. (See also ATOMIC WEIGHTS; CHEMISTRY; ELECTRICITY, CONDUCTION OF : in Gases; ISOTOPES ; QUANTUM THEORY.) BIBLIOGRAPHY.-E. N. da C. Andrade, The Structure of the Atom Bibliography.-E. N. da C. Andrade, The Structure of the Atom (1923) ; G. Birtwistle, The Quantum Theory of the Atom (1926), The New Quantum Mechanics (1928) ; N. Bohr, The Theory of Spectra and Atomic Constitution (1922) ; A. Sommerfeld, Atomic Structure and Spectral Lines (1923) ; J. D. Main Smith, Chemistry and Atomic Structure (1924) ; N. V. Sidgwick, The Electronic Theory of Valency (1927). (N. B.)