Equations · equation
Saha Ionization Equation
Astrophysics · 1920
- Equation
- n_{i+1}·n_e / n_i = (2g_{i+1}/g_i)·(2πm_e k_B T / h²)^(3/2)·e^(−χ/k_B T)
- Field
- Astrophysics
- Named After
- Meghnad Saha
- Year
- 1920
Symbols
n_i, n_{i+1} number densities of two adjacent ionization stages · n_e electron density · g statistical weights · m_e electron mass · T temperature · χ the ionization energy · k_B, h the Boltzmann and Planck constants
Significance
How hot matter decides how ionized to be — thermal equilibrium between atoms, ions and electrons. Saha wrote it for stellar atmospheres and it explained the spectral sequence at a stroke: O stars show ionized helium and M stars show titanium oxide not because they are made of different stuff but because they are at different temperatures. Cecilia Payne used it in 1925 to show the stars are overwhelmingly hydrogen. Applied to the whole universe it dates recombination: hydrogen stays ionized until about 3000 K, far below the 158 000 K that 13.6 eV suggests, because photons outnumber baryons a billion to one and the tail of the distribution keeps stripping electrons. That delay is why the microwave background was released at z ≈ 1100.
Spectral Types
Y-type Stars (Y Dwarfs)T-type Stars (T Dwarfs)K-type StarsB-type StarsM-type StarsG-type StarsA-type StarsL-type Stars (L Dwarfs)F-type StarsO-type Stars
Referenced by
constant
equation
event
instrument
theory
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