What Is the Rotational Temperature of CO Given Maximum Intensity at J'=11?

[richyw]

Homework Statement

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.

Homework 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.

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...

 

[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 $B$.

 

[richyw]

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