Band Theory of Metallic Bonding 

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Band Theory of Metallic Bonding
We are hopefully aware of the LCAO and Molecular Orbital Theory. If we consider the fact, the metallic lattice is a three-dimensional array of huge number of metal atoms. The large number of molecular orbitals formed remain closely packed and they form an energy band in which the energy levels are quasi-continuous. According to the Bloch theory, the energy bands are called Brillouin Zones. The Brillouin zones may be separated or overlapped.
The bands formed by the valence atomic orbitals bearing the valence electrons are called valence band. The energy level below which all the energy levels may be completely filled at 0K is referred to as Fermi level. Electrons from valence band can move to the next vacant band in the vicinity in presence of external electrical potential. The vacant band that provides the accommodation to the conducting electrons is called Conduction band. In case of partially filled valence band, like the case of alkali metals, the portion vacant acts as conduction band. Sometimes, the valence band overlaps with the conduction band as in the case of alkaline earth metals. But in some cases, a forbidden gap exists in between the valence band and conduction band.
Electrical Conductivity
When there is no potential, the net wave momentum of the electrons is zero because statistically there will same number of electrons moving with same speed but in opposite directions. When electrical potential is applied, electrons moving towards positive end increases leads to a net wave momentum to that direction. This results electrical conductivity. For electrical conductivity a conduction band is required just above the fermi level. In filled band no such redistribution is possible.
Conductors
To be a conductor of electricity the substance must have a partially filled valence band or overlapping valence and conduction band as we have discussed. In such cases, the forbidden energy gap is almost zero and electrons can move easily to the conduction band from valence band that leads to electrical conduction.
Insulators
In insulators the conduction band and valence band are widely separated and forbidden energy gap is much higher such that electrons can’t move to the conduction band from valence band at ordinary electrical potential. Generally, where the forbidden energy gap is greater than 3 electron volts, the substance is referred as an insulator.
Semiconductors
Obviously, you can guess that semiconductors will have the forbidden energy gap in between the conductors and insulators. Typically, the substances with forbidden energy gap in between 2 to 3 electron volts are called semiconductors.
There are two categories of semiconductors, #1. Intrinsic Semiconductors and #2. Extrinsic Semiconductors.
We will discuss about the both types in our next video. Till then, Alvida. Stay Home Stay Safe.
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