Simplified model for vibrational interactions

The frequency, which is independent of the elongation, is given by Hooke s law (expression 10.3) in which p, (kg) represents, as indicated, the reduced mass of the system. 

The vibrational energy of this simple model can vary in a continuous fashion. Following a short elongation Axg with respect to the distance from equilibrium Kib becomes  

The model above can be approximated to the chemical bond linking two atoms, on condition that the quantum theory governing species of atomic dimensions is employed. Because a bond whose frequency of vibration is v can absorb light radiation of an identical frequency, its energy will increase from the quantum A = hv. According to this theory, the simplified expression 10.8 will yield possible values for vib  

At room temperature, the molecules are still in the non-excited state y = 0, that is, (vib)o = l 2hv (energy at OK). Besides the standard transition Ay = +1, that corresponding to Ay = +2 and forbidden by this theory, appears weakly when the fundamental absorption band is particularly strong (for example, in the case of elongation vibrations in organic compounds containing a carbonyl bond C=0 (e.g. ketones or aldehydes). 

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