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Band Theory

A procedure analogous to our earlier discussion of molecular orbital theory of bonding in molecules was developed by Helix Block in 1928 to formulate a theory of metallic bond. In this model, the entire metal is considered as a big molecule and molecular orbitals are obtained which cover the entire metal.

In our earlier discussion on MO theory, we had observed that combination of two atomic orbitals (each contributed by one atom) combine to give two molecular orbitals (MOs), one bonding MO and the other antibonding MO. If we have three atoms contributing one AO each, the three AOs combine to give three MOs; one bonding MO, one non-bonding MO and the third an antibonding MO. On similar lines, it can be shown that combination of four AOs from four atoms gives rise to four MOs, two bonding MOs and two antibonding MOs. Similarly, if we have N toms, each atom contributing one atomic orbital [N is Avogadro’s number, 6.023 x 1023 atoms]. Combining to form N MOs. Since the number of MOs is very large, the energy levels of MOs are very close together that they form a continuous energy band. Such a close group of energy levels is called an energy band.

The molecular orbitals can no longer be treated as discrete energy levels, but are treated as an energy band. The formation of an energy band depends on:
(i)    the close proximity of large number of atoms, and
(ii)    the energy difference between pure atomic orbitals.

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