Calculating temperature of Hydrogen gas cloud

AI Thread Summary
The discussion focuses on calculating the temperature of an interstellar hydrogen gas cloud using the H-alpha line and the ratio of hydrogen atoms in excited states. Participants explore using Wien's displacement law and the occupation number, leading to initial temperature estimates of 1673.91K and 7782K, which are deemed too high. The correct approach involves the Boltzmann equation, which relates the populations of different energy states. Clarification on the Boltzmann equation is provided, aiding in understanding the necessary calculations. The conversation emphasizes the importance of using the right equations for accurate temperature determination.
rshalloo
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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?
 
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I believe you want the excitation equation, which relates the number of atoms in one energy state to the number in a different state.
 
tms said:
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?
 
Ahh yes that makes much more sense now. Thanks very much for your help :)
 
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