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Physics LibreTexts

8: Boltzmann's and Saha's Equations

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  • 8.1: Introduction
  • 8.2: Stirling's Approximation. Lagrangian Multipliers.
  • 8.3: Some Thermodynamics and Statistical Mechanics
  • 8.4: Boltzmann's Equation
    A dynamic equilibrium between collisional excitations and radiative de-excitations leads to a certain distribution of the atoms among their various energy levels. Most of the atoms will be in low-lying levels; the number of atoms in higher levels will decrease exponentially with energy level. The lower the temperature, the faster will be the population drop at the higher levels. Only at very high temperatures will high-lying energy levels be occupied by an appreciable number of atoms.
  • 8.5: Some Comments on Partition Functions
  • 8.6: Saha's Equation
    Saha function is a function of temperature and pressure, high temperature favoring ionization and high pressure favoring recombination. The equation tells us the relative numbers of the three types of particle (i.e. the degree of ionization) in an equilibrium situation when the number of ionizations per second is equal to the number of recombinations per second.
  • 8.7: The Negative Hydrogen Ion
    The word "ion" in the gas phase is often thought of as the positively charged remnant of an atom that has lost one or more electrons. However, any electrically charged atom (or molecule or radical), whether positively charged (as a result of loss of an electron) or negatively charged (having an additional electron) can correctly be called an "ion". In this section, we are interested in the negative hydrogen ion, H−, a bound system consisting of a proton and two electrons.
  • 8.8: Autoionization and Dielectronic Recombination
    One of the electrons can easily slip away from the atom without the absorption of any additional energy, thereby leaving behind an ion in an excited state. Such a process is called autoionization, and the levels or states concerned are autoionization levels or states. The converse process is quite possible. An ion in an excited state can capture a hitherto free electron, thus forming the neutral atom with two excited electrons. The process is dielectronic recombination. Downward transitions fro
  • 8.9: Molecular Equilibrium
  • 8.10: Thermodynamic Equilibrium


This page titled 8: Boltzmann's and Saha's Equations is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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