Model ion ratios from temperature and electron conditions quickly with unit choices. See fraction, logs, and wavelength; export for notes today in one click.
Enter your parameters and compute the ionization ratio and fraction.
| Case | T (K) | ne (m-3) | χ (eV) | gi | gi+1 | Expected trend |
|---|---|---|---|---|---|---|
| Warm, dense | 8000 | 1×1021 | 13.6 | 2 | 1 | Lower ionization, recombination favored |
| Hot, moderate | 15000 | 1×1020 | 13.6 | 2 | 1 | Higher ionization, exponential term dominates |
| Very hot, rare | 30000 | 1×1018 | 24.6 | 1 | 2 | Ionization rises, but depends on χ |
The calculator uses the Saha ionization equation for adjacent stages in thermal equilibrium:
A focused overview to support the calculator outputs.
Thermal ionization links microscopic physics to observable spectra. The Saha equation predicts the ratio of adjacent ion stages in a gas at equilibrium, combining translational phase space with an exponential Boltzmann factor. In astronomy it connects temperature and electron density to line strengths, helping estimate photospheric conditions in stars and nebulae.
The relation assumes local thermodynamic equilibrium, a Maxwellian electron distribution, and a well defined temperature shared by particles. It also treats ionization and recombination as balanced, so the plasma is not rapidly evolving. Departures from equilibrium, strong radiation fields, or nonthermal electrons can shift ion fractions away from Saha predictions.
Ionization responds strongly to temperature because the exponential term contains the ionization energy divided by kT. Small temperature increases can raise the ratio by orders of magnitude when kT approaches the threshold energy. This calculator displays both R and log10(R) to track that sensitivity without losing numerical clarity.
Electron density enters inversely, so higher ne favors recombination and reduces the ion ratio. In dense environments, collisions quickly restore equilibrium but the same density suppresses ionization by increasing available electrons. If you know electron pressure instead, the tool converts it to density using the ideal gas relation ne = Pe/(kT).
The degeneracy factor 2gi+1 and the ratio of partition like weights influence the prefactor, representing how many quantum states are accessible in each stage. When many excited levels matter, effective partition functions can replace simple g values. Using realistic weights improves predictions for complex atoms and partially ionized gases.
Ionization energy depends on the specific transition between stages and can vary by element and excitation. Laboratory tables usually list ground state thresholds in electron volts. If your population is dominated by excited states, an effective chi may be lower. The calculator accepts eV or joules and reports the converted value.
The ratio R = n(i+1)/n(i) indicates which stage dominates. The ionization fraction x = R/(1+R) provides a convenient two stage measure between 0 and 1. The thermal de Broglie wavelength shown here summarizes the electron quantum scale that appears inside the Saha prefactor.
Common uses include estimating hydrogen ionization in stellar atmospheres, tracking helium stages in hot plasmas, and building initial conditions for collisional radiative models. However, strong photoionization, rapid cooling, or optically thin nonequilibrium flows require kinetic treatment. Use Saha results as a baseline and validate with diagnostics when possible. In practice often.
It is the equilibrium number density ratio between two adjacent ion stages, n(i+1)/n(i), computed from temperature, electron density, statistical weights, and ionization energy.
It works best under local thermodynamic equilibrium with Maxwellian electrons and slow evolution, such as many stellar photospheres or dense laboratory plasmas.
The ratio is proportional to 1/ne, so increasing electrons favors recombination and shifts population toward the lower ion stage at the same temperature.
For simple systems, level degeneracies are fine. For multi level atoms at high temperature, partition functions better capture excited state populations and can noticeably change the ratio.
Temperature can be entered as Kelvin or kT in eV. Electron conditions can be density in m^-3 or cm^-3, or electron pressure in Pa or bar. Ionization energy can be eV or joules.
x = R/(1+R) maps the two stage mixture onto a 0–1 scale. Values near 0 indicate mostly stage i, while values near 1 indicate mostly stage i+1.
Real plasmas may be photoionized, time dependent, or nonthermal. Line formation also depends on excitation, opacity, and radiative transfer, so Saha alone may not match observations.
Compute ionization balance quickly, accurately, and ready to export.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.