Gaussian emission lines

[RHK]

Homework Statement

The spectroscopic observation of an interstellar gas cloud shows emission lines H (λ=6563 A), Hβ λ=4862 A) e OI (λ=1304 A), each one with a gaussian profile of the kind:

$g(\nu)=A e^[-\frac{(\nu-\nu_0)^2}{2\sigma^2}]$

Per Hα si osserva $σ_{Hα} = 1.2 \times 10^{10} Hz$.
Supposing that gas is in thermodynamic equilibrium at a temperature T, uniform in the whole cloud, determine:

1) the T value;
2) the $σ_{OI}$ value;
3) the Full Width at Half Maximum of the Hβ line.

Homework Equations

The Doppler broadening $Δ\nu/\nu = v/c$.
The Virial temperature: $1/2 m v^2 = 3/2 k T$.

The Attempt at a Solution

Regarding only the first point, can I proceed with the above-mentioned formulas?
If yes, I find a temperature of T≈2500 K, that is an order of magnitude higher then the typical temperature of interstellar clouds...
If not (and this is), why not?

Thanks in advance :)

PS: I don't like this formulas editor et all :D

 

[RHK]

Any ideas please?