D. S. Rozhdestvensky. Spectral Analysis and the Structure of Atoms. Proceedings of the State Optical Institute. Vol. I, no. 6, pp. 87 + 3 unnumbered. State Publishing House, Petrograd, 1920.

This booklet is a reproduction of a speech delivered by the author at the annual meeting of the Optical Institute in 1919. Its first pages are devoted to a survey of those achievements of the theory of atomic structure for which physics is indebted chiefly to Bohr and Sommerfeld; the remaining—and larger—part of the booklet is devoted to the author’s own considerations, in which he attempts to approach the solution of the difficult question of the structure of the complex atoms of the alkali metals.

It is known that Bohr’s theory applies to the atom of neutral hydrogen (nucleus and 1 electron) or to an ionized helium atom. In the latter case we are dealing, in principle, with the same scheme, and the difference is due only to the fact that in helium the charge of the nucleus is equal to \(2e\). If from these simplest cases we pass to the next element—lithium—then insuperable mathematical difficulties immediately arise (the problem of four bodies). The same, of course, must also be said of the remaining alkali metals, where the number of interacting bodies will be still greater.

D. S. Rozhdestvenskii attempts to circumvent these difficulties by an indirect route. His method, in a few words, consists in the following. All alkali metals are monovalent. This means that each of them has one valence electron in the outer orbit and, according to Bohr, only this valence electron can jump from one orbit to another, thereby giving rise to various spectral lines. Let us dwell on the concrete example of lithium. Suppose its valence electron is on one of the far possible orbits. It will be attracted by the nucleus with charge \(+3e\) and repelled by the two electrons situated on the inner ring. Calculation shows that in this case we shall make only a very small error if we assume that both these electrons are situated at the center, coincident with the nucleus. Then the resultant charge acting on the valence electron will be equal to \(+3e+(-2e)=+e\), and we again obtain a hydrogen-like atom. From this the author derives an important consequence: “the distant orbits of lithium will differ little from the distant hydrogen orbits, and the total energy which the electron possesses in these orbits will likewise be almost identical in the atoms of hydrogen and lithium.”

All these considerations, however, lose their force when we turn to orbits closely approaching the inner ring of lithium. Here it is no longer possible to identify the inner electrons with the nucleus, and, on the other hand, the complex interactions of all three electrons may completely change the character of the motion of the system.—D. S. Rozhdestvenskii proceeds in this case as follows. Starting from the formulas of spectral series (somewhat improved by him), he calculates, with the aid of very simple considerations, the relative magnitudes of the energy of the valence electron on various orbits and compares them with the corresponding energies on hydrogen orbits. As a result of all the calculations and comparisons it turns out that in the atoms of alkali metals we have as many possible orbits as in hydrogen, and that the perturbations introduced by the presence of inner electron rings, although they distort these orbits, do not do so to such an extent that they cannot be recognized.

From consideration of the absorption spectrum the author draws the following picture of the structure of the lithium atom in the unexcited state: the inner two electrons revolve in a circle of radius \(1.92 \cdot 10^{-9}\) cm, making \(2.49 \cdot 10^{15}\) revolutions per second. The valence electron moves along

an elongated ellipse, whose major semi-axis is 11 times greater than the radius of the inner circle, i.e. \(= 2.11 \cdot 10^{-8}\) cm. Of course, near the perihelion this elliptical orbit is distorted under the influence of the inner electrons.

From the further contents of the booklet we note the interesting considerations on the origin of doublets, which the author explains by the internal Zeeman phenomenon (the splitting of lines in the magnetic field of the inner rings).

The booklet is written throughout with great ease and is read with much interest.

É. Shpolsky.