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 toJ'e^{-aJ'(J'+1)}wherea =\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!