In solids, bands result from the overlap of atomic orbitals, much as molecular orbitals result from the overlap of atomic orbitals in small molecules. According to the MO theory of diatomic molecules, molecular orbitals form when an atomic orbital from one atom overlaps with an atomic orbital from a second atom.
A lower-energy bonding molecular orbital is formed by the in-phase addition constructive interference of the two atomic arbitals, and a higher-energy antibonding molecular orbital is formed by addition of two atomic orbitals of opposite phase.
This idea can be applied to larger molecules. However, because one molecular orbital is generated for each atomic orbital used in its construction , three or more molecular orbitals are created when of three or more atomic orbitals overlap.
In this picture, we do not need to consider the 1s, 2s and 2p "core" electrons of Na or the orbitals in which they are placed , because these core electrons are strongly bound to individual atoms, and do not contribute significantly to bonding.
Figure 1 shows the proliferation of molecular orbitals that are formed as an increasing number of Na atoms are combined to make the solid. When a very large number of atoms are combined, a "3s band" is formed.
The energy spread of this band is determined by energy difference between the most strongly bound "bonding orbital" and the highest energy "antibonding'" orbital.
The number of individual molecular orbitals within the band is equal to the number of contributing atomic orbitals.
Since each atom contributes a single 3s orbital, the number of molecular orbitals in the 3s band of a piece of solid sodium containing N atoms is N. According to the Pauli principle, each of these N orbitals can contain 2 spin-paired electrons. Many of the physical properties that we think of as being characteristic of metals are consistent with the band description given above.
The most characteristic property of any metal is high electrical conductivity. This property is particularly well explained using a band theory model. When an electron absorbs energy from an electric field, it is excited into an unfilled molecular orbital, constructed from all of the atomic orbitals in the entire metal.
As a result, this orbital is totally delocalized. Therefore, it provides a kind of electronic highway throughout the entire metal, allowing charge to be transported with great ease.
The band picture also explains why metals are ductile and malleable. Since the sea of delocalized electrons can immediately adjust to any deformation that occurs in the overall crystal structure, the integrity and strength of the new deformed structure can be immediately restored.
Finally, the characteristic shininess of metals can be well understood in band theory terms. Figure 2 illustrates the kind of electronic transitions that can occur in a metal having a band only partially filled with electrons. Absorption can take place over the entire visible spectrum. The vertical arrows in Figure 2 represent transitions that take place when photons 1 of energy, h n , collide with the metal, transferring energy to one of the electrons, which is then promoted to an orbital of higher energy.
The transitions shown in this figure range from those of low energy, characteristic of red and IR photons, to those of much higher energy, characteristic of blue and UV photons. However, metals do not just absorb photons: they re-radiate them. Since metals are electrical conductors, absorption of an electromagnetic wave light causes the relatively free valence electrons within the metallic structure to oscillate at the frequency of the exciting radiation.
This oscillation causes the metal to re-radiate light of the same frequency as the incoming wave by a mechanism that is just the reverse of that which allowed light to be absorbed in the first place.
This ability to re-radiate photons accounts for the high reflectivity, and thus shininess , of most metals.