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NEW EXPERIMENTS WITH A MOLECULAR BEAM USING O. STERN’S METHOD
G. S. Landsberg, Moscow.
The striking results obtained by Stern and Gerlach in observing the deflection of molecular beams in a nonuniform magnetic field are generally known1. At present Stern, at the Institute of Physical Chemistry of the University of Hamburg, has undertaken a systematic development of problems that can be investigated by the molecular-beam method. Six papers from this series have already been published. Some of them are devoted to a description of the considerably improved apparatus and methods of calculation (the accuracy of adjustment has been increased approximately 2000-fold in comparison with the original experiments), and an extensive program of work has been outlined. In some of them new results are reported.
In the dissertation of A. Löw2, new, extremely careful measurements have been made of the splitting of beams of K, Na, and Tl. Confirming the earlier results, they make it possible to establish, with an accuracy of up to 2%, that the value of the projection of the magnetic moment of the atom onto the direction of the magnetic field for the elements of the first group is equal to one Bohr magneton. The photograph appended makes it possible to judge the quality of the experiment. Part a reproduces the trace of the beam in the absence of a magnetic field, part b—with the magnetic field switched on. It is interesting to compare these photographs with the original results of Stern and Gerlach (“Advances in the Physical Sciences,” 5, no. 1), where splitting can be observed only in the middle part of the field.
In another Hamburg dissertation, Brede3 made a successful attempt to determine the magnetic moment of atomic hydrogen. As is known, ordinary hydrogen is diamagnetic, whereas a hydrogen atom, from Bohr’s point of view, should possess a definite magnetic moment, i.e., be paramagnetic. Obviously, the diamagnetism of H\(_2\) is explained by the presence of two electrons mutually compensating their magnetic moments. To investigate the hydrogen atom it was necessary to use a beam of atomic hydrogen, the preparation of which, after the work of Langmuir, presents no great difficulty. Brede obtained atomic hydrogen by forcing a jet of ordinary hydrogen to pass slowly through a long (about 2 m) platinum tube heated by electric discharges. The jet of the resulting atomic hydrogen was admitted into the apparatus, where the necessary low pressure was maintained by the continuous operation of powerful pumps. The scheme of the remaining arrangement is the same as in the experiments of Stern and Gerlach; only all slits and diaphragms, of course, had to be made of glass, for atomic hydrogen, on contact with metal, quickly associates. The bands
the electromagnet were also placed outside the apparatus. As the recording plate, a glass plate coated with MoO₃, slightly moistened, was used. At the places where atomic hydrogen comes into contact with molybdenum oxide, it vigorously reduces the metal and leaves a dark trace, clearly visible against a light background. The plates were fastened to a loop. After the action of the atomic beam (for 2–3 hours) in the presence of a field had left a double trace on the plate, the magnetic field was turned off, the plate was turned through a certain angle, and the already unsplit beam left a new trace, going at an angle to the first. The exposure time in the absence of the magnetic field could be limited to 20 minutes. The reproduced photograph shows the observed picture. Examples of the plate make it possible to calculate, for the hydrogen atom, a magnetic moment also equal to one Bohr magneton.
The results presented, impeccable from the experimental point of view, bring to mind certain theoretical considerations with which they compel agreement with the new quantum mechanics.
As is known, the manifold spectral regularities, above all the anomalous Zeeman effect and the regularities in alkali and X-ray doublets, led to the formulation of the hypothesis of the rotating electron, according to which every electron belonging to an atom, in addition to charge and mass, possesses a magnetic moment equal to one Bohr magneton.¹) In particular, this hypothesis makes it possible to explain the existence of the anomalous Zeeman effect in hydrogen, thus compelling one also to ascribe to the hydrogen electron a magnetic moment of one Bohr magneton. The hydrogen nucleus, like the cores of the alkali metals, has no intrinsic magnetic moment. For alkali cores constructed after the type of the noble gases, we naturally suppose, as for the latter, a mutual compensation of the magnetic moments due to the individual electrons. Thus there remain only two sources of magnetism for hydrogen and the alkalis: the intrinsic magnetic moment of the single valence electron and the magnetic moment due to the motion of this electron in its orbit. According to Landé’s normalization, this latter motion in the principal orbit, which for the elements of the 1st group is an \(S\)-orbit, leads to the formation of a magnetic moment also of one magneton, so that the total magnetic moment of the system is two Bohr magnetons. (Taking into account the compensation of the moments in connection with [[unclear: damaged line]] the Bohr theory.) Further, as is known, the “quantum” condition is that, under the action of a magnetic field, the atom can be oriented only at an angle of \(60^\circ\) and \(120^\circ\) to it, i.e. the projection of the magnetic moment of the atom onto the direction of the field is \(= \pm 1\) Bohr magneton. To such an orientation there corresponds the observed splitting of the trace of the beam into two components. Orientation perpendicular to the magnetic field, which would give a third—undeviated—component, Landé’s theory was likewise compelled to forbid.
Otherwise, and formally much more simply, the phenomenon is treated from the point of view of the normalization that follows from the new quantum mechanics. Under this normalization
¹) Cf. the article by Ya. I. Frenkel, “The Rotating Electron,” Uspekhi fizicheskikh nauk, 7, 308, 1927.
the term \(S\) corresponds to the azimuthal quantum number \(K = 0\). In other words, the mechanical and magnetic moment of such an orbit is zero and, consequently, the total magnetism of the atom is determined solely by the intrinsic magnetism of its optical electron. From this point of view the simple character of the \(S\)-terms is established of itself, since the electron is not under the orienting action of the orbit and therefore cannot assume various positions to which different values of the energy of the atomic system would correspond.
In exactly the same way the question of the absence of paramagnetism in He, and a number of other problems, including the famous paradox of the “crossed fields,” disappear of themselves. From the point of view under consideration, the Stern and Gerlach phenomenon is interpreted naturally. In an external magnetic field the electron can assume only two positions—parallel and antiparallel to the field—and therefore the whole beam is split into two, as is indeed observed experimentally.
The principal difficulty standing in the way of this fruitful conception lies in the plane of the old “naive” theory of the atom. For the requirement \(K = 0\) is the requirement that the orbit have no angular momentum, i.e., from the point of view of the model, that the electron move along a rectilinear orbit passing through the nucleus (oscillatory motion). This, of course, is incompatible with the model representations from which Heisenberg’s mechanics fundamentally departs. However burdensome this lack of visualizability may be, it is hardly possible on this ground to renounce all the advantages of the new interpretations. This does not mean, of course, that visualizability should be neglected altogether. But, while using these visual representations as most useful guides, one should not raise them to the role of fetishes.