Saha ionization equation

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Saha ionization equation

(sah -hah) An equation, put forward by the Indian physicist M.N. Saha in the 1920s, that gives the ratio of the number density (number per unit volume) of ions, N +, to the number density of neutral atoms, N 0, in the ground state in a system of atoms, ions, and free electrons at a given temperature. The system is in equilibrium so that the rate of ionization is equal to the rate of recombination of electrons and ions. The equation can be given in the form:
N +/N 0 = A (kT )3/2 eI /kT /N e
A is a constant, k is the Boltzmann constant, T the thermodynamic temperature, N e the number of electrons per unit volume (the electron density), and I is the ionization potential of the atom. The equation also gives the ratio N 2+/N +, N 3+/N 2+, etc., if I is replaced by the second (I 2) or the third (I 3) ionization potentials, etc.

The equation shows that the higher the temperature, the more highly ionized a particular atom will be. It can therefore be used to find the relative numbers of neutral, singly ionized, doubly ionized atoms, etc., in stars of known temperature and electron density. See also Boltzmann equation.