Thermal Radiation of Gases and Spectra of Luminaries

(1). Megh Nad Saha. On the problems of temperature radiation of gases. Philosophical Magazine 41, 267, 1921.

(2) Megh Nad Saha. Versuch einer Theorie der physikalischen Erscheinungen bei hohen Temperaturen mit Anwendung auf die Astrophysik. Zeitschrift für Physik, 6, 40, 1921.

The basic idea of a series of interesting works by the Indian physicist Saha is as follows. Until recently, thermodynamics, in its applications, dealt chiefly with such physical processes as melting and evaporation and with the chemical processes of molecular dissociation. What, however, will occur when a gas consisting of atoms is heated? The modern theory of atomic structure leads to the necessity of partial ionization of the gas in this case. In heated calcium vapor, for example, the following process must take place:

\[ Ca \rightleftarrows Ca^{+} + e \tag{1} \]

where \(Ca^{+}\) is an ionized calcium atom, \(e\) an electron. The dependence of the concentrations of the three components of process (1) on the temperature and pressure at equilibrium can be found by Nernst’s method.

To find the energy required for ionization, one may use the values of the ionization potential of the elements, carefully determined recently in the works of Franck, Hertz, Mac Lennan, and others. Such a calculation, however, will not be entirely correct. According to Bohr’s theory, intermediate stable stationary states exist between the normal and ionized atom; therefore it is possible that, upon heating, the atom is not ionized at once, but passes into an intermediate stable state, or else is ionized, but not from the normal state, rather from an intermediate one. At present there are not yet data for a quantitative account of these complications; one must therefore confine oneself only to the simplest, approximate scheme.

These simple considerations allow Saha to solve, at least qualitatively, a whole series of physical and astrophysical problems.

1. It may be expected in advance that the higher the resonance potential (and at the same time also the ionization potential) of an element, the more difficult it is to excite the radiation of a line spectrum by purely thermal means. This is confirmed by experiment. Such permanent gases as \(H_2\), \(He\), \(Ne\), \(A\), \(N_2\), \(O_2\), etc., do not emit a line spectrum, as the experiments of Pringsheim and others show, even at the highest laboratory temperatures.

On the other hand, the spectra of such elements as \(J\), \(Br\), \(As\), \(S\), \(Se\), \(Sb\), of the alkali and alkaline-earth metals, are obtained already at comparatively low temperatures, as King has shown. This series almost coincides with the series of ionization potentials. The ionization potential of the permanent gases is especially high. Thus the old dispute over the existence of a special “temperature excitation” and “electrical excitation” of the luminescence of elements is resolved. The nonconformity to Kirchhoff’s rule of side series lines is explained by the fact that the number of atoms whose valence electrons are situated on two, three, etc., quantum orbits is negligible at low temperatures.

1. Many investigators have vainly tried to detect ionization when a gas is heated. A large part of the experiments was carried out with mercury. But mercury has a high ionization potential, 10.45 V. Calculation (by Nernst’s method) shows that the ionization of mercury even at \(2000^\circ\) and at a pressure of 0.1 atm. will be practically imperceptible. On the other hand, recently Hemsalech discovered the ionization of vapors of \(Li\), \(Na\), \(K\), \(Rb\), \(Cs\) at temperatures of \(2200\)—\(3000^\circ\) (absolute scale). All these elements have a small ionization potential.

1. As is known, elements in the ionized state emit changed spectra (the so-called “spark” spectra). Thus, for example, the line 422.7 μμ belongs to \(Ca\), the line 393.4—to \(Ca^+\). From the presence of the latter line we can judge the presence of ionized calcium in a given gas mixture. The ratio of the intensities of the two lines makes it possible to judge the degree of ionization. For example, in the flame of King’a (2500°) the ratio of the brightnesses of the lines is 15, in the voltaic arc (4000°)—0.8, in the solar photosphere 0.02 (7500°), and in the spectrum of Sirius (10000°) practically 0.

2. Lockyer and Jansen were the first to obtain a photographic image of the chromosphere of the sun, and from the image one can judge the brightness of the lines at various heights of the chromosphere. Analysis of the image gave unexpected results. In the higher layers of the chromosphere the brightest lines belong to \(Ca^+\), and not to hydrogen; on the other hand, in the high layers of the chromosphere the “spark” lines of heavy metals are especially noticeable. To explain this fact Lockyer proposed the strange hypothesis of an increase in temperature with height. Meanwhile, an analysis of the equilibrium between neutral and ionized atoms, on the basis of Nernst’s theorem, makes it possible to conclude that the percentage of ionized atoms increases not only with an increase in temperature, but also with a decrease in pressure. For example, for calcium the percentage of ionized atoms with decreasing pressure at \(T = 6000^\circ\) changes as follows (Table 1):

TABLE 1.

Taking this circumstance into account and, moreover, recalling that the ionization potential \(H\)—17.1 V, and \(Ca\)—6.12 V, we obtain a simple explanation of the spectrum of the chromosphere.

1. Spectroscopic investigations reveal the presence on the sun of only 32 elements out of the 92 known on earth. In Saha’s opinion, the reason for this is not that 60 elements are absent from the sun, but solely that in the spectral region of the sun accessible to us, under the thermodynamic conditions of the solar surface (7000—7500°, 0.1—1 atm. pressure), only the lines of 32 elements are excited. For example, \(Rb\) and \(Cs\) must be completely ionized under these conditions, but the corresponding spectral lines of ionized \(Rb\) and \(Cs\) lie in the ultraviolet region, inaccessible to observation. The sodium lines are very intense in the solar absorption spectrum, but they are absent in the upper layers of the chromosphere, since there, owing to the negligible pressure, sodium is completely ionized. As a consequence of the enormous ionization of the upper layers of the chromosphere, the outer shell of the solar atmosphere must consist of electrons, which undoubtedly play a primary role in the phenomena of terrestrial magnetism and the aurora borealis.

2. Analysis of stellar spectra makes it possible to construct a quite rational system of “spectral types of stars,” often introduced empirically by astronomers. The analysis may be based, in a first approximation, on several lines of the most typical elements \(H\), \(He\), \(Ca\), \(Sr\), \(K\). For illustration we present selections from one of Saha’s tables (Table 2):

TABLE 2.

Generally speaking, the typical stellar spectra of all classes from \(O\) to \(N\) serve as an illustration of those physical phenomena that unfold in the transition from 4000° to 30,000°.

On the basis of the considerations set forth, one must abandon the idea held by many astronomers of constructing a theory of the evolution of chemical elements analogous to Darwin’s theory. Stellar spectra reveal to us only the thermodynamic state of their surfaces, and not their chemical composition. The spectra of the so-called “proto-elements” of astronomers in the great majority of cases can be identified with the spectra of ionized atoms of ordinary elements.

S. Vavilov.