How do you find the temperature of an HII region?

Danielk010
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Homework Statement
Determine whether a spectral line is seen in emission, absorption, or not at all, and explain why. The vantage point is the surface of the Earth.

e. An HII region in front of a background quasar. The quasar has a brightness temperature of 75 k.
Relevant Equations
##T < T_{B_{v_o}}## = absorption line (eq 1)
##T > T_{B_{v_o}}## = emission line (eq 2)

##\tau = L * n * \sigma##
##\sigma = 6.3*10^{-18} cm^2##
##E = 13.6 eV##
## T_{B_{v_o}} = T (\tau \gg 1)##
I first approached this problem with the idea that I could try to find the temperature of the HII region given that we already know the background temperature. Still, I am stuck on finding the region's temperature.

A second approach was to try to find if the cloud is optically thick, which would mean the spectral line is neither. I know from a table in my textbook that the cross-section for the ionized cloud is ##6.3*10^{-18} cm^2##, but I don't know L, the distance a particle travels, or n, the number of particles in the cloud. Maybe I can assume L is very far given the vantage point is on the surface of Earth, but then I don't know what n would be.

I am a bit stuck on where to start. I am assuming the answer is going to be more conceptual and less numeric but I don't get why they would give the background temperature then.

Thank you for any help.
 

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