Saha Equation

The Saha equation can be expressed as

N_q+1N_e / N_q  = [(2πm_ekT)^3/2/h³][2u_q+1(T)/u_q(T)]exp(-I_q / kT),

where

        N_q+1 = total number of particles per unit volume in the q+1^th ionization state of the element under consideration, (N_q+1 =  Σ _r N_q+1,r),
        N_q = total number of particles per unit volume in the q^th ionization state of the element under consideration, (N_q =  Σ _r N_q,r),
        N_e = total number of free electrons per unit volume,
        u_q+1(T) = Σ _r g_q+1,r exp(-χ_q+1,r / kT) is the partition function for the q+1^th ionization state, the r^th term of which is proportional to the number
                        of particles (per unit volume) in the r^th level of excitation,
        u_q(T) = Σ _r g_q,r exp(-χ_q,r / kT) is the partition function for the q^th ionization state, the r^th term of which is proportional to the number of
                     particles (per unit volume) in the r^th level of excitation,
        g_q,r = the stistical weight of the r^th excited level of the q^th ionization state,
        χ_q,r = the excitation energy of the r^th excited level with respect to the ground level of the q^th ionization state,
        I_q = the ionization energy of the q+1^th ionization state with respect to the ground state of the q^th ionization state,
        m_e = the electron mass = 9.1093897 ´ 10^-28g,
        h = Planck's constant = 6.6260755 ´ 10^-27erg s,
        k = Boltzmann's constant = 1.380622 ´ 10^-16 erg/K = 8.61779 ´ 10^-5 eV/K, and
        T = the temperature expressed in Kelvins.

Note that the Saha equation can also be written

N_q+1P_e / N_q  = [(2πm_e)^3/2/h³](kT)^5/2[2u_q+1(T)/u_q(T)]exp(-I_q / kT),

where P_e = N_ekT is the electron pressure in dyn cm^-2.

The logarithmic form of the Saha Equation is

log (N_q+1 / N_q) = -θI_q [eV] + 2.5 log T - 0.48 + log [2u_q+1(T)/u_q(T)] - log P_e,

where θ º 5040/T.