The Equilibrium of Atoms and Electrons

The Equilibrium of Atoms and Electrons.—From the cases we have taken up, wTe see that the kinetics of collisions forms a complicated and involved subject, just as the kinetics of chemical reactions does. Since this is so, it is fortunate that in cases of thermal equilibrium, we can get results by thermodynamics which are independent of the precise mechanism, and depend only on ionization potentials and similarly easily measured quantities. And as we have stated, thermodynamics, in the form of the principle of microscopic reversibility, allows us to get some information about the relation between the probability of a direct process 

A mixture of electrons, ions, and atoms forms a system similar to that which we considered in Chap. X, dealing with chemical equilibrium in gases. Equilibrium is determined, as it was there, by the mass action law. This law can be derived by balancing the rates of direct and inverse collisions, but it can also be derived from thermodynamics, and the equilibrium constant can be found from the heat of reaction and the chemical constants of the various particles concerned. The heats of reaction can be found from the various ionization potentials, quantities susceptible of independent measurement, and the chemical constants are determined essentially as in Chap. VIII. Thus there are no new principles involved in studying the equilibrium of atoms, electrons, and ions, and we shall merely give a qualitative discussion in this section, the statements being equivalent to mathematical results which can be established immediately from the methods of Chap. X. 

The simplest type of problem is the dissociation of an atom into a positive ion and an electron. By the methods of Chap. X, we find for the partial pressures of positive ions, negative electrons, and neutral atoms the relation 

From Eq. (4.2), we see that the equilibrium constant is zero at the absolute zero, rising very slowly until the temperature becomes of the 

From Eq. (4.3), wo see that as the pressure is reduced at constant temperature, the dissociation becomes greater, until finally at vanishing pressure the dissociation can become complete, even at ordinary temperatures. This is a result of importance in astrophysics, as has been pointed out by Saha. In the solar atmosphere, there is spectroscopic evidence of the existence of rather highly ionized elements, even though the temperature of the outer layers of the atmosphere is not high enough for us to expect such ionization, at ordinary pressures. However, the pressure in these layers of the sun is extremely small, and for that reason the ionization is abnormally high. 

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