Saha Equation

a formula for the degree of thermal ionization α of a gas—that is, for the ratio of the number of ionized atoms to the total number of atoms present. First stated by M. Saha in 1920 for the description of processes in stellar atmospheres, the equation was derived from general thermodynamic considerations and deals with the case of a weakly ionized gas in a state of thermodynamic equilibrium. The equation has the form

where T is the absolute temperature, p is the pressure of the gas, W_i is the ionization potential of the gas’ atoms, g_a and g_i are the statistical weights of the neutral atom and the ion, respectively, m is the mass of an electron, k is the Boltzmann constant, and h is Planck’s constant.

The Saha equation is only approximately valid because its derivation rests on the assumption that only three types of particles are present: neutral atoms, singly ionized ions, and electrons. Multiple ionization, excited atoms, and the presence of impurities are not taken into account. Also not considered is the interaction of the gas with the wall. Such interaction can result in surface ionization and in the ionization of the gas by electrons ejected from a hot wall. Despite these limitations, the Saha equation is applicable to many cases where α ≪ 1.