On the Natural Oscillations of Atoms in Bohr’s Model in the Infrared Part of the Spectrum in Connection with Specific Heat at High Temperatures

(Gerda Laski. Ultrarote Eigenfrequenzen zweiatomiger Bohr’scher Gasmoleküle und die Spezifische Wärme bei hohen Temperaturen. Phys. ZS. 20, p. 263—1919).

Until recently, the Bohr–Debye model of \(H_2\) was the only model whose predicted properties had been compared with experiment. For this model it was assumed that two positive nuclei were situated at a definite distance from one another, while in the plane perpendicular to this line and bisecting the distance between the nuclei, two electrons revolved in a circle, remaining at all times at the ends of a diameter. Atoms more complex than hydrogen must be represented by more complex models, and several possibilities for the arrangement of the electrons can be imagined; calculations therefore become more difficult. The oscillations that can most readily be calculated are those that the nuclei will execute if displaced from their positions of equilibrium. Since these oscillations are performed by masses whose magnitudes are of the order of atomic masses, it is natural to suppose that these oscillations will give infrared radiations. Thus, from the Rutherford–Bohr theory it is easy to obtain natural oscillations in the infrared part of the spectrum. From natural oscillations in the infrared part of the spectrum, one can derive, according to Nernst, the values of the specific heat; therefore, by comparing the theoretically calculated value of the specific heat with its experimentally determined value, one can test theoretical ideas about the structure of the molecule.

Calculations of the specific heat of hydrogen obtained in this way, for temperatures from \(1686^\circ\) to \(2541^\circ\), give very good agreement with experiment.

To obtain a similar agreement between theory and experiment for \(N_2\) and \(O_2\), the author constructs the model of the \(N\) molecule as follows: the model consists of two positive nuclei with charges \(7\epsilon\)¹), at a distance \(d = 9.1 \cdot 10^{-9}\) cm from one another. Near each nucleus lies an “inner” ring of small radius, consisting of two electrons; the outer ring, consisting of 10 electrons, is two-quantum and has a radius \(8.05 \cdot 10^{-9}\) cm. Its plane lies perpendicular to \(d\), dividing the molecule into 2 symmetric parts. To this model of the molecule there corresponds a model of the atom \(N\), in which around the nucleus there are two rings of electrons—one one-quantum with two electrons and another outer two-quantum ring with 5 electrons. According to the author, the molecule \(O_2\) consists of two nuclei with charges \(8\epsilon\); around each nucleus are placed close rings, each consisting of 2 electrons, and one ring with 12 electrons; the plane of this latter ring divides the distance between the nuclei in half, dividing the molecule into 2 symmetric parts. Corresponding to this molecule \(O_2\), the atom \(O\) consists of a nucleus and two rings; on the inner (one-quantum) ring are located 2 electrons and on the outer (two-quantum) ring 6 electrons.

P. Lazarev.