sess4s - 4. Reaction equilibria 4.1 The Saha equation If...

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4. Reaction equilibria 4.1 The Saha equation If particles and radiation are in equilibrium with themselves and each other, we call their state Thermodynamic Equilibrium, and the spectra are given by a Planckian for the radiation and a Fermi distribution (a Maxwellian if the density is not too high) for the particles. If the particles are only in equilibrium with themselves, but not with the radiation, we speak of Local Thermodynamic Equilibrium (LTE), in which the radiation spectrum is not a priori known, but the particle spectrum is still a Fermi, resp. a Maxwellian, distribution. In Local Thermodynamic Equilibrium the distribution of atoms with ionization state i over the various energy states m is proportional to exp( χ i,m /kT ), where χ i,m is the excitation energy of state m relative to the ground state. Then N i,m N i, 1 = g i,m g i, 1 exp( χ i,m kT ) (4 . 1) where g i,m are the statistical weights of state ( i, m ), that is the number of independent ar- rangements of the atomic electrons that give the same ionization state and energy level. After summing over all m we ±nd N i = s m N i,m = N i, 1 g i, 1 s m N i,m g i,m exp( χ i,m kT ) = N i, 1 g i, 1 u i ( T ) (4 . 2) N i,m N i = g i,m u i ( T ) exp( χ i,m kT ) where u i ( T ) = s m g i,m exp( χ i,m kT ) (4 . 3) is called the level partition function . We can derive the Saha equation that, using the level partition sums, can be written as an equation for the ionization equilibrium. N
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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sess4s - 4. Reaction equilibria 4.1 The Saha equation If...

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