ast403_saha equation notes

# ast403_saha equation notes - IONIZATION SAHA EQUATION Let...

This preview shows pages 1–2. Sign up to view the full content.

IONIZATION, SAHA EQUATION Let the energies of two states, A and B , be E A and E B , and their statistical weights g A and g B , respectively. In LTE (Local Thermodynamic Equilibrium) the number of particles in the two states, N A and N B , satisfies Boltzman equation: N A N B = g A g B exp [ ( E A E B ) /kT ] . (i . 1) Now, we shall consider two ions, “i” and “i+1”, of the same element. The ionization potential, i.e. the energy needed to ionize “i” from the ground state is χ , and the statistical weights of the ground states of the two ions are g i and g i +1 , respectively. The number densities, [ cm - 3 ], of the two types of ions and free electrons are n i , n i +1 , and n e , respectively. We shall use the Boltzman equation (i.1) to estimate the number ratio n i +1 /n i . The statistical weight of an ion in the lower ionization state to be used in the equation (i.1) is just g i . The statistical weight of an ion in the upper ionization state is g i +1 multiplied by the number of possible states in which a free electron may be put. As we know, in every cell of a phase space with a volume h 3 there are two possible states for an electron, because there are two possible orientations of its spin. h = 6 . 63 × 10 - 27 erg s is the Planck constant. The energy of a free electron with a momentum p with respect to the ground state of an ion in a lower ionization state is E = χ + p 2 / 2 m . The number of cells available for free

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern