How do you find the temperature of an HII region?

[Danielk010]

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.