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I am wondering how many free electrons per baryon and how many free electrons per atom there are in the solar photosphere. This number depends on the abundances of the various atoms found in the photosphere as well as each atom's ionization potential.

The book "Introduction to Stellar Astrophysics" by Boehm-Vitense, vol. 2, 1997 reprint, on page 76 claims that one out of every $10^4$ hydrogen atoms are ionized, so hydrogen is mostly neutral in the photosphere; however, there are other heavier elements with lower ionization potentials. Boehm-Vitense goes through and calculates the fraction of ionization of iron but calculations for only two species present in the photosphere can hardly be considered comprehensive.

Whether you calculate these numbers yourself or provide a summary of a reference (with a link to that reference if possible) that has more details about ionization in the photosphere it will be appreciated.

My guess is that, since hydrogen has such a low degree of ionization, the number of electrons per baryon and per atom will be small, since hydrogen is the majority constituent of the photosphere.

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The degree of ionization in the photosphere varies with depth of course, but overall it is small. Table 1 of the Bilderberg Continuum Atmosphere (Solar Physics, 3, 5, 1968) gives the pressure and the electron pressure at various optical depths in a comprehensive model. The ratio of the pressure gives the Ne/Ntotal. At optical depth = 1 at 5000 Angstroms, Pgas = 1.412E5 (cgs) and Pe = 6.239E1. The ratio is 4.4E-4. The hydrogen ionization, also given in the table is 4.07E-4. The model assumes Helium abundance of 0.1 which is off a bit from the modern number of 0.087.

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