Saha ionization equation

The Saha ionization equation, also known as the Saha–Langmuir equation, is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics and is used to explain the spectral classification of stars. The expression was developed by the Indian astrophysicist Meghnad Saha in 1920, and later (1923) by Irving Langmuir.Saha had concentrated on the marginal appearances and disappearances of absorption lines in the stellar sequence, assuming an order of magnitude for the pressure in a stellar atmosphere and calculating the temperature where increasing ionization, for example, inhibited further absorption of the line in question owing to the loss of the series electron. As Fowler and I were one day stamping round my rooms in Trinity and discussing this, it suddenly occurred to me that the maximum intensity of the Balmer lines of hydrogen, for example, was readily explained by the consideration that at the lower temperatures there were too few excited atoms to give appreciable absorption, whilst at the higher temperatures there are too few neutral atoms left to give any absorption. ..That evening I did a hasty order of magnitude calculation of the effect and found that to agree with a temperature of 10000° for the stars of type A0, where the Balmer lines have their maximum, a pressure of the order of 10−4 atmosphere was required. This was very exciting, because standard determinations of pressures in stellar atmospheres from line shifts and line widths had been supposed to indicate a pressure of the order of one atmosphere or more, and I had begun on other grounds to disbelieve this. The Saha ionization equation, also known as the Saha–Langmuir equation, is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics and is used to explain the spectral classification of stars. The expression was developed by the Indian astrophysicist Meghnad Saha in 1920, and later (1923) by Irving Langmuir. For a gas at a high enough temperature and or density, the thermal collisions of the atoms will ionize some of the atoms, making an ionized gas. When several or more of the electrons that are normally bound to the atom in orbits around the atomic nucleus are freed, they form an independent electron gas cloud co-existing with the surrounding gas of atomic ions and neutral atoms. In turn, this generates an electric field, where the motion of charges generates currents, making a localised magnetic field, and creates the state of matter called plasma. The Saha equation describes the degree of ionization for any gas in thermal equilibrium as a function of the temperature, density, and ionization energies of the atoms. The Saha equation only holds for weakly ionized plasmas for which the Debye length is large. This means that the screening of the Coulomb interaction of ions and electrons by other ions and electrons is negligible. The subsequent lowering of the ionization potentials and the 'cutoff' of the partition function is therefore also negligible.