As outlined in my previous post I'm trying to get a better understanding of spectroscopy by doing a few problems and I was wondering if anyone could tell me if I'm going wrong anywhere in my methods of working them out.

I know the forum rules say don't post multiple question topics but I can't seem to find anyway to modify/edit my posts or topic titles and the subject is slightly different, can mods tell me if it's acceptably different and deserving of it's own thread?

The fundamental absorption of HF occurs at 4138.32cm^{-1}. The first overtone of this absorption was measured at 7618.53cm^{-1}. Using these data calculate the :

(i) Equilibrium oscillation frequency *W*_{e}

(ii) Anharmonicity parameter *X*_{e}

(iii) Maximum vibrational level for HF

(iv) Bond dissociation energy (BDE) of HFMy attempts:

Parts (i) and (ii):

I would use the equation

for an anharmonic oscillator. I would plug in values of 0, 1 and 2 for

*v* for its different transitions.

I would then get the difference in

*E* from

*v=0* to

*v=1* and

*v=0* to

*v=2* giving me two equations:

w

_{e}(1-2x

_{e}) = 4138.32cm

^{-1}2w

_{e}(1-3x

_{e}) =7618.53cm

^{-1}I would then solve these equations simultaneously to get values for w

_{e} and x

_{e}Am I right in having 3 transitional states for v i.e. 0, 1 and 2 even though I only have two wavenumber values i.e. 4138.32cm

^{-1} and 7618.53cm

^{-1}?

Part (iii):

To get the maximum vibrational level would it be right to say that the maximum level of

*v* is when:

*W*_{e}(1 - 2X_{e}(v_{max} + 1)) = 0 :delta: Eand

v_{max} =(1/2X_{e}) - 1I can then plug in the

*X*_{e} value obtained earlier to get

*v*_{max}For that question is it enough to get the maximum level of

*v* or should I go further and get the maximum energy of that state by plugging all the values into

*e*_{vib} = (v+1/2)W_{e }- X_{e}(v+1/2)^{2}W_{e} ?

Part (iv):

To get the BDE I would just convert the energy value obtained for v

_{max} to kJ using 1cm

^{-1} = 11.958 J mol

^{-1}