[TheUnfocusedOne]

Hey all,

I'm really stuck on a problem:

The J = 2 <- J=1 microwave absorption is observed near 42723MHz for 14NF3 and 42517MHz for 15NF3. Derive the rotational constants for 14NF3 and 15NF3.

I'm starting to think it's impossible. The molecules are prolate symmetrical tops, which means that B=C, and you can find B by using v = B J(J+1). But finding A seems damn near impossible, especially since you aren't given any information regarding bond lengths or angles (asked for in the next questions).

The only equation I can find relating B or C is through E = BJ(J+1) + (A-B)k^2. You can't do dE since the term with the A cancels out, and I'm not given a value for either energy level. I also don't have the molecular wave functions for the molecule, so I doubt I have to calculate it from scratch.

What am I missing??

[Corribus]

Because of the ΔK = 0 selection rule, you can't determine the other rotation constant from a single transition line.  You have to use isotopic substitution and make assumptions about similarity of structure.  I don't remember exactly how to do this off the top of my head, but I believe you use B and the formula for inertial mass to determine the molecular structure.  Usually you can't do this with B alone because there are two different axes of rotation (you would need A/C and B to determine structure for a symmetric top) but if you assume the structures are the same for the two isotopically substituted versions, you can use the two values of B in some way to determine the structure.  Which then can be used to determine the respective A values.  Like I said I don't remember how to do this exactly, but I remember doing a problem like this back in the day and I think I recall using that procedure to do it.  So I'd look at the formula for relating the moments of inertia to atomic positions and see if you can't figure out a way to use the two B values to do that.

I'd have to check through my old notes to jog my memory better, and I can do it tomorrow if you haven't figured it out by then. 

By the way, are you sure NF₃ is prolate? 

[TheUnfocusedOne]

Well, regardless of whether it's prolate or oblate, I was still going to have a constant I couldn't solve for. Good thought though.

Turns out, I wasn't supposed to find the third constant  . The question was ambiguously worded in my opinion.

Thanks for the response though!