Developed by the Indian astrophysicist Meghnad Saha in 1920, this formula describes the degree of ionization of a gas as a function of the temperature T, density, and ionization energy. Meghnad Saha (मेघनाथ साहा) (October 6, 1893 – February 16, 1956) was an Indian astrophysicist. ... 1920 is a leap year starting on Thursday (link will take you to calendar) Events January January 7 - Forces of Russian White admiral Kolchak surrender in Krasnoyarsk. ...

Let X = n_e / n be the ionization fraction, i.e., the electron density relative to the total density of atoms and ions. Then one form of the Saha equation is

where h is Planck's constant and I is the ionization energy. Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ...

There are several different ways of writing the Saha equation; another form is given by

where r and r+1 refer to the ionization states (r+1 being one state more ionized than r), e refers to an electron, and where n is the number density, λ_T is the thermal de Broglie wavelength, g is the degeneracy, χ is the ionization potential, k_B is the Boltzmann constant, and T is the temperature. This equation is useful for determining what the ratio of particles in two different ionization levels is. The wavelength is the distance between repeating units of a wave pattern. ... The word degeneracy has more than one meaning: In general, degeneracy means reverting to an earlier, simpler, state In mathematics, a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

This form of the equation arises from the equation

where Z denotes the partition function, N represents the number of atoms of the gas (divide by volume to get the number density), and the subscript r refers to a particular ionization state, r+1 refers to the next higher ionization state, and e refers to an electron. This, in turn, arises from the equillibrium condition for the chemical potentials: In statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in thermodynamic equilibrium. ... The chemical potential of a thermodynamic system is the change in the energy of the sytem when an additional constituent particle is introduced, with the entropy and volume held fixed. ...

μ_r = μ_r+1 + μ_e

This equation simply states that the potential for an atom of ionization state r to ionize is the same as the potential for an electron and an atom of ionization state r+1; the potentials are equal, therefore the system is in equillibrium and no net change of ionization will occur.

External links

• a detailed derivation
• lecture notes