# Estimating Rotational Temperature

1. Apr 21, 2014

### richyw

1. The problem statement, all variables and given/known data

An R-branch of a band of a $^1\Sigma - ^1\Sigma$ of CO has its maximum intensity at J'=11. The internuclear distance is 1.1 Ǻ. Estimate the rotational temperature.

2. Relevant equations

My notes don't even really define what rotational temperature is. They say that the Line strength of the $J' \rightarrow J'-1$ line in the R branch is proportional to$$J'e^{-aJ'(J'+1)}$$where$$a =\frac{hc B}{kT}$$and B is the rotational constant. My notes also say that this value goes through a maximum value of J' that depends on temperature, so by observing the strongest line I can get the rotational temperature.

3. The attempt at a solution

I have been stuck for awhile on this. Initially I thought that I would need to take the derivative of this function with respect to J', set it equal to zero, plug in J'=11 and then solve for a. But I don't think this is the correct method now...

2. Apr 21, 2014

### electricspit

I'm pretty sure you're in my class.

I'm pretty sure also that is the correct method, because it worked out quite nicely for me. You should end up with a solution for $T$ in terms of $B$ and the other constants you know. You can use the distance between the atoms to find the moment of inertia, then find $B$.

3. Apr 21, 2014

### richyw

thanks! I think initially I forgot to square the internuclear distance which gave me a really weird result. Good luck with your studying!