Publication

Ionisation equilibrium in the electron-proton gas

Nicolas Macris
1990
Journal Articles

Abstract

Using Fefferman's analysis of the quantum electron-proton gas, we give a rigorous proof of ionization equilibrium in this system. Ionization equilibrium phases are obtained as low-density and low-temperature limits, letting the chemical potentialmgr(T) approach the ground-state energy of the hydrogen atom as the temperatureT tends to zero. The rate of ionization is determined by the slope ofmgr(T) atT=0 and is correctly given by the Saha formula. We also discuss a simpler model where a single quantum particle interacts with a classical gas of hard spheres.

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https://infoscience.epfl.ch/entities/publication/1697db24-8cc7-4909-8e75-59991420691e

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Nicolas Macris
1990
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1697db24-8cc7-4909-8e75-59991420691e

About this result

Related concepts (32)

Self-ionization of water

The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, OH−. The hydrogen nucleus, H+, immediately protonates another water molecule to form a hydronium cation, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.

Ionization energy

In physics and chemistry, ionization energy (IE) (American English spelling), ionisation energy (British English spelling) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, positive ion, or molecule. The first ionization energy is quantitatively expressed as X(g) + energy ⟶ X+(g) + e− where X is any atom or molecule, X+ is the resultant ion when the original atom was stripped of a single electron, and e− is the removed electron.

Fermi gas

A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.

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Ionisation equilibrium in the electron-proton gas

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