Theory of Electronic Band Spectra.

Just as there are electronic energy levels in an atom, there are electronic energy levels in molecule also. However there are no simple formula available for the energies of these electronic levels (except for the hydrogen like atoms).

Electronic spectra are obtained when the electrons in a molecule are excited from a lower electronic energy level to a higher level. However, as the electronic transition is accompanied by vibration and rotational transition, the total energy of the molecule in any state is the sum of the electronic energy, vibration energy and rotational energy.

If E_e E_v and E_r represent the electronic energy, vibration energy and rotational energy respectively of the molecule in the initial state before transition and E_e’, E_v’ and Er the corresponding values in the final state after transition, then we have

Energy of the molecule in the initial state:
                                E = Ee + Ev + E_r
Energy of the molecule in final state:
                                E = Ee' + Ev' + E_r'
    Energy change involved in the electronic transaction will be given by
                               
But according to Planck’s quantum theory
                                  

As for a particular electronic transition (so that  remains constant), and for a particular vibration transition (so that remains constant), can have different values (due to different rotational transition within the same vibration energy change of the same electronic energy level)a number of closely spaced lines are obtained. This constitutes a “band”. For each vibration transition, separate band will be obtained. Thus due to different vibration transition for a particular electronic transition, a set of bands is obtained, called the “band group” or “band system”. Each electronic transition will give a band system and hence the complete electronic spectra transition will give a band system and hence the complete electronic spectra. Involving different electronic transition gives rise to a series of band groups. Thus the” electronic band spectrum” obtained for a gaseous molecule is quite complex.

Inspire of the complex nature of the electronic band spectra, these are preferred over the other types because these are obtained in the visible and ultraviolet regions so that these can be easily photographed and studied.

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