All Topics  
Saha ionization equation

 

 
   Email Print
   Bookmark   Link
 

 

Saha ionization equation
 
 
  Topics Saha ionization equation Topic Home

The Saha ionization equation, also known as the Saha-Langmuir equation, was developed by the Indian astrophysicist Megh Nad Saha in 1920, and later (1923) by Irving Langmuir
Irving Langmuir

Irving Langmuir was an United States chemistry and physics. His most noted publication was the famous 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N....
. One of the important applications of the equation was in explaining the spectral classification of stars. The equation is a result of combining ideas of quantum mechanics and statistical mechanics.

For a gas at a high enough temperature, the thermal collisions of the atoms will ionize some of the atoms. One or more of the electrons that are normally bound to the atom in orbits around the atomic nucleus will be ejected from the atom and will form an electron gas that co-exists with the gas of atomic ions and neutral atoms. This state of matter is called a plasma
Plasma (physics)

In physics and chemistry, plasma is a partially ionized gas, in which a certain proportion of electrons are free rather than being bound to an atom or molecule....
.






Discussion
Ask a question about 'Saha ionization equation'
Start a new discussion about 'Saha ionization equation'
Answer questions from other users
Full Discussion Forum



Encyclopedia


The Saha ionization equation, also known as the Saha-Langmuir equation, was developed by the Indian astrophysicist Megh Nad Saha in 1920, and later (1923) by Irving Langmuir
Irving Langmuir

Irving Langmuir was an United States chemistry and physics. His most noted publication was the famous 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N....
. One of the important applications of the equation was in explaining the spectral classification of stars. The equation is a result of combining ideas of quantum mechanics and statistical mechanics.

For a gas at a high enough temperature, the thermal collisions of the atoms will ionize some of the atoms. One or more of the electrons that are normally bound to the atom in orbits around the atomic nucleus will be ejected from the atom and will form an electron gas that co-exists with the gas of atomic ions and neutral atoms. This state of matter is called a plasma
Plasma (physics)

In physics and chemistry, plasma is a partially ionized gas, in which a certain proportion of electrons are free rather than being bound to an atom or molecule....
. The Saha equation describes the degree of ionization of this plasma as a function of the temperature, density, and ionization energies of the atoms. The Saha equation only holds for weakly ionized plasmas for which the Debye length
Debye length

In plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers electric field screening in plasma physics and other conductors....
 is large. This means that the "screening" of the coulomb charge of ions and electrons by other ions and electrons is negligible. The subsequent lowering of the ionization potentials and the "cutoff" of the partition function
Partition function (statistical mechanics)

In statistical mechanics, the partition function Z is an important quantity that encodes the statistics properties of a system in thermodynamic equilibrium....
 is therefore also negligible.

For a gas composed of a single atomic species, the Saha equation is written:

where:

  • is the density of atoms in the i-th state of ionization, that is with i electrons removed.
  • is the degeneracy
    Degenerate energy level

    In physics two or more different physical states are said to be degenerate if they are all at the same energy level. Physical states differ if and only if they are linearly independent....
     of states for the i-ions
  • is the energy required to remove i electrons from a neutral atom, creating an i-level ion.
  • is the electron density
    Electron density

    Electron density is the measure of the probability of an electron being present at a specific location.In molecules, regions of electron density are usually found around the atom, and its bonds....
  • is the thermal de Broglie wavelength
    Thermal de Broglie wavelength

    In physics, the Thermal de Broglie wavelength is defined for a freeideal gas of massive particles in equilibrium as:where* h is Planck's constant...
     of an electron
  • is the mass of an electron
  • is the temperature
    Temperature

    In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
     of the gas
  • is the Boltzmann constant
    Boltzmann constant

    The Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant NA:...
  • is Planck's constant


In the case where only one level of ionization is important, we have and defining the total density n  as , the Saha equation simplifies to:

where is the energy of ionization.

The Saha equation is useful for determining the ratio of particle densities for two different ionization levels. The most useful form of the Saha equation for this purpose is

,

where Z denotes the partition function
Partition function (statistical mechanics)

In statistical mechanics, the partition function Z is an important quantity that encodes the statistics properties of a system in thermodynamic equilibrium....
. The Saha equation can be seen as a restatement of the equilibrium condition for the chemical potential
Chemical potential

In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
s:

This equation simply states that the potential for an atom of ionization state i to ionize is the same as the potential for an electron and an atom of ionization state i+1; the potentials are equal, therefore the system is in equilibrium and no net change of ionization will occur.

External links

  • from University of Utah
    University of Utah

    The University of Utah is a public university research university in Salt Lake City, Utah. One of ten institutions that make up the Utah System of Higher Education and Utah's premier research school currently enrolls 21,526 undergraduate and 6,684 graduate student students and has 1,419 regular Faculty members....
     Physics Department
  • from University of Maryland
    University of Maryland, College Park

    The University of Maryland, College Park is a public research university located in the city of College Park, Maryland in Prince George's County, Maryland outside Washington, D.C....
     Department of Astronomy
  • Saha, Megh Nad; , Proceedings of the Royal Society of London, Series A, Volume 99, Issue 697 (May 1921), pp. 135–153
  • Langmuir, Irving; and Kingdon, Kenneth H.; , Physical Review, Vol. 22, No. 2 (August 1923), pp. 148–160