Vibration Rotational Spectra
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Vibration Rotational Spectra
Pure vibration spectra are obtained only for liquids where rotational motions hindered due to interactions between the liquid molecules. However in case of gaseous molecules, as the energy required for rotation is much less than that required for vibration, the vibration motion is always accompanied by rotational motion and hence we do not have a pure vibration spectra ; instead we have a vibration-rotational spectra lying in the infrared region.As rotational motion and vibration motion take place independent of the total energy of the molecule may be taken as the sum of the rotational energy and the vibration energy (which is much larger than the former). Thus

or it can be written as

Expressing in terms of wave numbers, it can be written as

But from eqn.


Substituting these values in eqn. we get

Here


From eqn. it is clear that in the same vibration level (so that

When a transition takes place form a level with quantum number



Restricting to the transition form


Putting (1-2xe)


(i) For transition with

(ii) For transition with

Combining equations we get

where m = J+ 1 in eqn. and m = -(J' +1) in eqn. As J = 0,1,2,3......, this means that in eqn. m =



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