1 x 104 Temperature (K)

2 x 104

The ratio of electrons to the total number of hydrogen atoms (neutral plus ion), for an electron density appropriate to stars like the Sun.

Table 3.1.1 Ionization energies (eV).

Atom Singly ionized Doubly ionized

The Saha equation has the same exponential energy dependence as the Boltzmann distribution. However, there is an additional factor of TH2. This comes from the fact that a free electron has more states available to it at higher Tk than at lower Tk. In addition there is a factor of ne on the left. This is because a higher abundance of electrons leads to a higher rate of recombinations, driving down the fraction of atoms that are ionized. Just as we did with the excitation temperature in the Boltzmann equation, we can define an ionization temperature Tj, which makes the Saha equation correct, even if the gas is not in thermodynamic equilibrium.

In this equation ne is the number of electrons from all sources, since any electron can combine with a hydrogen ion (for example) no matter where that electron came from (hydrogen, helium, etc.) In many situations, virtually all of the ions are hydrogen. That is because hydrogen is by far the most abundant element, and because the next most abundant element, helium, is very hard to ionize. In that case, the number of electrons is equal to the number of positive ions, n+, a o u a r to

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