Need help calculating the size of the Stromgren sphere

[warfreak131]

Homework Statement

A stromgren sphere is the sphere surrounding a star where the photons from the star can ionize the gas. So the radius of the sphere is the extent from the star in which the gas is ionized. For a fully ionized (idealized, for this question) sphere of gas, the number of protons would equal the number of electrons in the sphere.

(Please look at the attached image to see the full question, it has a large equation that would be very difficult to type out)

Homework Equations

The Attempt at a Solution

The equation includes n_en_p, and these two quantities should be equal, so can I just rewrite it as n_e²? I figure I will do an integral to find the number of electrons in time, but how can I apply that to the number density? I am assuming that n_e and n_p stand for number of electrons and protons, so how can I calculate that to work out to 10^3/cm^3?

Or is my technique crrect at all? Would my integral be definite or indefinite? And since the temperature term doesn't deal with n_e or t, can I pull it out and be left with a simple differential equation?

Also, what is radiative equilibrium and how would I calculate it?

 

[warfreak131]

bump, anybody please?