Calculating temperature of Hydrogen gas cloud

[rshalloo]

Homework Statement

The H-alpha line corresponds to a transition between the 2nd and 1st excited states of hydrogen, and has a wavelength of 656.3nm. The ratio of the number of atoms in these two states in an interstellar cloud of atomic hydrogen is 2x10^-6. Find the temperature of the cloud

Homework Equations

I was thinking maybe something to do with wiens displacement law
$\frac{h f}{k T}=2.822$
or maybe occupation number
$n_{i}=\frac{1}{e^{\frac{h c}{k T \lambda}}-1}$

The Attempt at a Solution

I kind of took a stab in the dark with the occupation number and got 1673.91K and then the same with wiens law and got 7782K both of which I'm guessing are slightly too large for a hydrogen cloud.

Could someone please point me in the correct direction?

 

[tms]

I believe you want the excitation equation, which relates the number of atoms in one energy state to the number in a different state.

 

[rshalloo]

I believe you want the excitation equation, which relates the number of atoms in one energy state to the number in a different state.

I'm not sure we've covered that? (am attempting previous exam papers so it might have been on the course before) unless there's also another name for such an equation?

 

[tms]

Also called the Boltzmann equation, but Boltzmann had many equations. Try this page:

http://spiff.rit.edu/classes/phys440/lectures/boltz/boltz.html

 

[rshalloo]

Ahh yes that makes much more sense now. Thanks very much for your help :)