Inglis–Teller equation

The Inglis–Teller equation represents an approximate relationship between an energy level and the electron number density. This equation is related to the Stark effect in which spectral lines are split explicitly due to the presence of an electric field. The equation was derived by David R. Inglis and Edward Teller in 1939.

The equation is directly related to astrophysics as the electron densities of stars are determined using this equation. Since the Stark effect shifts spectral lines, for some energy level n, the splitting is equal to the difference between the adjoining energy level. Beyond this level, spectral lines merge.

Electron density and the merging energy level relationship for hydrogen atom is given by;

$\log(N_i+N_e)=23.491 - 7.5\log(n_m)\,,$

where, N_i= no: of positive ions per cm³, N_e= no: of negative electrons per cm³, n_m= last observable energy level of the Balmer series.

Further reading

• "Electron density in the emission line region of Wolf-Rayet stars" – Y.P Varshni
• Ionic Depression of Series Limits in Cne-Electron Spectra (Inglis, D. R.; Teller, E.). Astrophysical Journal, vol. 90, p. 439.