Use Saha-Boltzmann statistics to get the relative number densities

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SUMMARY

The discussion focuses on the application of Saha-Boltzmann statistics to determine relative number densities in astrophysical contexts. The Saha equation is highlighted as a critical tool for calculating electron pressure, denoted as P_e, which is directly related to electron number density (n_e) and temperature (T). Participants emphasize the interdependence of these variables, noting that n_e must be known or estimated to effectively utilize the Saha equation for accurate calculations.

PREREQUISITES
  • Understanding of the Saha equation and its application in astrophysics
  • Familiarity with concepts of electron pressure and number density
  • Knowledge of thermodynamic principles, particularly relating to temperature (T)
  • Basic grasp of statistical mechanics, specifically Saha-Boltzmann statistics
NEXT STEPS
  • Research methods to estimate electron number density (n_e) in various astrophysical environments
  • Study the derivation and implications of the Saha equation in plasma physics
  • Explore the relationship between temperature (T) and electron pressure (P_e) in stellar atmospheres
  • Investigate applications of Saha-Boltzmann statistics in modern astrophysical research
USEFUL FOR

Astrophysicists, researchers in plasma physics, and students studying statistical mechanics will benefit from this discussion, particularly those focused on the behavior of ionized gases and stellar atmospheres.

Zapped17
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Homework Statement
Use Saha-Boltzmann statistics to get an idea of the relative number densities of H, H+, H−, and H(n = 3).
Gather information from Gray’s book concerning the partition functions (hint: with its two electrons H−
is He-like; H+ is a naked proton, so U(p) = 1), the electron pressure, and so on. Assume T = 5772 K
(S 0 = 1, as Gray labels it in the relevant plots) and solar surface gravity. Take care with the units!
· What do you learn from comparing N(H−) and N(H, n = 3)?
Relevant Equations
The Saha equation N_i+1/N_i
for i:s energy levels.
When I am using the Saha equation, how i am suppose to know the electron pressure?
Which are required to calculate the ration?
Since: P_e = n_ekT (electron pressure and n_e is related to each other, but n_e is also unknown based on my understanding).
 

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