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: \[(n_{i+1}/n_{i}) n_{\rm{e}} = 2\lambda^{-3}(g_{i+1}/g_{i}) \exp[-(\epsilon_{i + 1} - \epsilon_{i})/kT]\] where \(n_{i}\) is the number density of atoms with \(i\) electrons removed, \(g_{i}\) is the degeneracy of the \(i^{\rm{th}}\) state, \(\epsilon_{i}\) is the ionization energy of the \(i^{\rm{th}}\) state, \(n_{\rm{e}}\) is the number density of electrons, \(\lambda\) 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: \[\lambda = \sqrt{\frac{h^{2}}{2\uppi m_{\rm{e}} kT}}\] where \(h\) is the Planck constant, \(k\) the Boltzmann constant, \(T\) temperature, and \(m_{\rm{e}}\) 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 (https://doi.org/10.1515/pac-2019-0203)