Fermi, E.; Sulla Quantizzatione del Gas Perfetto Monoatomico / Quantization of the Monatomic Perfect Gas
Rend. Lincei 3, 145 (1926);
Enrico Fermi. /it Collected Papers (Note e Memorie) v.I. Italy 1921-1938. The University of Chicago Press - Accademia Nazionale dei Lincei, Roma (1962).
(translation into Russian) Enrico Fermi. Nauchnye Trudy. I. 1921-1938 Italiya. (pod red. B.Pontecorvo), Nauka, Moskva, 1971.
The author's object is to demonstrate a method of quantizing a perfect gas which does not depend on hypotheses concerning the statistic behaviour of its molecules. Numerous attempts have recently been made to establish the equation of state of a perfect gas. The various formulae differ from each other and from the classical equation only for very low temperatures and very high densities. But that is where the deviations of the laws of real from those of perfect gases are most marked, and as, under
experimental conditions, the deviations from the equation of state pV = kT, due to the degeneration of the gas, are, though not negligible, always somewhat less than those due to the fact that the gas is real and not perfect, the former have hitherto been masked by the latter. With a more complete knowledge of the forces acting between the molecules of a real gas it may be possible to separate the two deviations, and thus decide experimentally between the various theories of the degeneration of
perfect gases. In order to quantize the molecular motion of a perfect gas, Sommerfeld's rules, subjecting the molecules to a system of forces such that their motion becomes periodic and thus quantizable, must be applicable. But to calculate systems containing elements not distinguishable from each other, Sommerfeld's rules need to be supplemented. For the choice of a hypothesis the behaviour of the heaviest hydrogen atoms, all containing more than one electron, must be examined. In the deep portions
of a heavy atom the forces acting between the electrons are very small compared with those exercised by the nucleus. Sommerfeld's rules here lead to the conclusion that in the normal state of the atom many of the electrons would be situated in an orbit of a total quantum 1. Observation shows, however, that the ring K is saturated when it contains two, ring L when it contains eight electrons, etc. This fact has been interpreted by Stoner and Pauli The atom cannot thus contain two electrons whose
orbits are characterized by the same quantum numbers, i.e. an electronic orbit is "occupied'' when it contains one electron. Applying a similar hypothesis to the quantization of a perfect gas containing at most one molecule whose motion is characterized by certain quantum numbers, the author proposes to show that it leads to a perfectly consistent theory of such quantization, accounting for the reduction of the specific heat at low temperatures and leading to the exact value for the constant of
entropy. Full mathematical details are reserved for a future paper. (Science Abstracts, 1926, 1609. E. F. ).
Related references See also A. Einstein, Sitzber. Pr. Akad. Wiss. 22 (1924) 261;
A. Einstein, Sitzber. Pr. Akad. Wiss. 23 (1925) 1;
A. Einstein, Sitzber. Pr. Akad. Wiss. 23 (1925) 18;
E. C. Stoner, Phil. Mag. 48 (1924) 719;
E. Fermi, Nuovo Cim. 1 (1924) 145;
W. Pauli, Z. Phys. 31 (1925) 765;
A. Einstein, Sitzber. Pr. Akad. Wiss. 23 (1925) 49;
Invention of statistics for ensembles of particles obeying Pauli principle.