IUPAC - Saha’s ionization equation (08542)

Saha’s ionization equation

synonym: Saha–Langmuir equation

https://doi.org/10.1351/goldbook.08542

Equation that relates the ionization state of an element present in a gas in thermal equilibrium to the temperature and the pressure of the medium.

Notes:

For a gas composed of a single atomic species, the Saha equation is written: $(n_{i + 1} / n_{i}) n_{e} = 2 λ^{- 3} (g_{i + 1} / g_{i}) \exp [- (ϵ_{i + 1} - ϵ_{i}) / k T]$ where $n_{i}$ is the number density of atoms with $i$ electrons removed, $g_{i}$ is the degeneracy of the $i^{t h}$ state, $ϵ_{i}$ is the ionization energy of the $i^{t h}$ state, $n_{e}$ is the number density of electrons, $λ$ is the thermal de Broglie wavelength of an electron, $k$ is the Boltzmann constant, and $T$ is the thermodynamic temperature of the gas.
The thermal de Broglie wavelength is given by: $λ = \sqrt{\frac{h^{2}}{2 π m_{e} k T}}$ where $h$ is the Planck constant, $k$ the Boltzmann constant, $T$ temperature, and $m_{e}$ the mass of an electron.

Source:
PAC, 2021, 93, 647. (Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)) on page 732 [Terms] [Paper]

Citation: 'Saha’s ionization equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.08542 RIS BibTex EndNote

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Saha’s ionization equation