Month of Equations: What Does Saha's Equation Really Mean?

Meaning of the equation:

Saha's equation tells the degree of ionization of a gas in thermal equilibrium by relating it to the pressure and temperature of the gas.

Developed by an Indian astrophysicist Meghnad Saha in 1920, Saha's equation is a useful result of combining the quantum mechanics and statistical mechanics to explain the spectral classification of stars. This equation depicts the dependence of ionization of a gas on various physical parameters such that :

Dependence on ionization energy : As the temperature of a gas is raised, the degree of ionization of a gas remains low until the ionization energy is greater than the gas temperature (evident from the exponential factor).

Dependence on temperature: Afterwards, the degree of ionization i.e., the ratio of number density of ions to the number density of neutral atoms of a gas in thermal equilibrium increases abruptly with an increase in temperature and the gas becomes a plasma (composed of ions, electrons and few neutral atoms).

Dependence upon number density of ions: When an atom becomes charged, it may recombine with an electron and become a neutral again. So, as the number of electrons increase, the ionization ratio decreases. In the simplest hydrogen plasma, the number of electrons are considered to be equal to the number of ions and hence, as the number density of ions increase in a plasma, the rate of neutralization of ions is enhanced too and the ionization ratio decreases.

Let us now try to understand the physical significance of this equation:

The stellar interiors and atmospheres, gaseous nebulae, and much of the interstellar hydrogen are plasmas. In fact nearly 99% of the universe is considered to be in a plasma state. It is indeed very surprising but we may actually say that luckily the Earth where we live is in the remaining 1% of the universe where plasmas do not occur naturally. However, as soon as we leave the Earth, we may again encounter plasma.

Saha's equation depicts that a gas attains a plasma state at extremely high temperatures and low number densities of charged particles. It is because of this reason that plasmas exist naturally in astronomical objects with temperature of millions of degrees and very low number densities of atoms around 1 per cm cube and due to their natural occurrence, plasma is considered to be the fourth state of matter.