What is Band Model of the Metallic Bonding?

We know that molecular orbitals are formed by overlapping of atomic orbitals. This model uses the molecular orbital approach.

For example the two molecular hydrogen molecules (H2) are formed by overlapping of two atoms of hydrogen atom. The energy of the two orbitals is different. One orbital will have higher energy and the other orbital will have lower energy. The energies of the orbitals were represented by the energy level whose magnitude vary with the nuclear distance between the two atoms.

The difference between the energy of two molecular orbital at equilibrium internuclear distance is given as AB.

In general we can say that if ‘n’ number of atomic orbitals overlaps then they will form ‘n’ molecular orbitals. The necessary condition for overlapping is that the atomic orbitals should have the same symmetry and should associate with the same or similar amount of energy.

Let us take example of valence band of sodium metal:
A metal lattice consists of large number of atoms. Due to this there will be large number of molecular orbitals and hence there will be continuous energy band of extremely large number of energy levels which are formed by overlapping of symmetrical atomic orbitals having the similar amount of energy.

Each energy level in sodium metal is able to hold two electrons. There will be overlapping of 3s and sp orbitals of sodium metal.

The completely occupied molecular orbitals are formed by overlapping of inner orbitals having same symmetry and same energy. They are occupied by the inner electrons. There is a considerable energy gap between the inner orbitals bands and the valence orbital bends. This is necessary because only then the electrons from the completely filled inner orbitals energy band will not get excited to the valence band energy. The molecular orbitals are common for all the bands of atoms in the lattice. This is due to the common electrons in the energy levels of the energy bands. And they belong to the same lattice. We can say that they are completely delocalized.

As there is only single electron in the sodium atom in the 3s orbital, so only half of the 3s energy level band will be occupied by the electrons. This property of sodium atom makes the sodium metal a good conductor of electricity. Similarly all the alkali metal’s valence energy band is half filled so they are good conductor of electricity.

Category: Chemical Bonding

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