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Band theory is a theoretical model in solid-state physics that defines the states of electrons in solid materials that can only have energy values within defined ranges. In a solid, the behaviour of an electron (and consequently its energy) is influenced by the behaviour of all other particles. In contrast, an electron’s behaviour in free space, where it can have any energy, is quite different. The ranges of electron energies that can exist in a solid are known as allowable bands. Permitted bands are energy ranges between two allowed bands; electrons within the solid are not allowed to have these energies. The band theory is the foundation of solid-state electronics technology and accounts for many of the electrical and thermal properties of solids. The range of energies permissible in a solid is connected to the discrete authorised energies—the energy levels—of single, isolated atoms.
The discrete energy levels of individual atoms are disrupted by quantum mechanical phenomena when they are joined to create a solid, and the many electrons in the collection of individual atoms occupy a band of levels in the solid known as the valence band. The conduction band is a band of typically empty levels formed by empty states in each individual atom. Electrons in a solid can transfer from one energy level in a given band to another in the same band or another band, usually crossing a prohibited energy gap in the process, just as electrons at one energy level in an individual atom might shift to another vacant energy level.
Band theory of metallic bonding:
Due to the lack of a bandgap, metals have a partially filled valence band and a partially filled conduction band. The hypothesis predicts that metals conduct extraordinarily well (both heat and electricity) and is universally recognized. We know that atomic orbitals overlapping generate molecular orbitals. This model employs the molecular orbital technique. By overlapping two hydrogen atoms, two molecular hydrogen molecules (H2) are created. The two orbitals have different energies. The energy level of one orbital will be higher, while the energy level of the other will be lower. The energy level, whose magnitude varied with the nuclear distance between the two atoms, reflected the orbital energies.
The difference in energy between two molecular orbitals at equilibrium internuclear distance is denoted by the letter AB. In general, when n atomic orbitals overlap, n molecular orbitals are formed. For overlapping to occur, the atomic orbitals must have the same symmetry and be associated with the same or similar amount of energy.
Molecular orbital band theory :
In chemistry, molecular orbital theory (MO theory or MOT) is a way for describing the electronic structure of molecules using quantum mechanics. In the early twentieth century, it was proposed. In molecular orbital theory, electrons in a molecule are not ascribed to distinct chemical interactions between atoms, but are instead viewed as moving under the influence of the atomic nuclei across the molecule. Quantum mechanics describes the spatial and kinetic features of electrons as molecular orbitals, which surround two or more atoms in a molecule and contain valence electrons between them. MOT provides a decentralised, global view of chemical bonding.
According to MO theory, each electron in a molecule can be found anywhere because quantum conditions allow electrons to migrate under the influence of an arbitrarily large number of nuclei as long as they are in eigenstates allowed by particular quantum principles. When electrons are excited with enough energy via high-frequency light or other means, they can transition to higher-energy molecular orbitals. UV radiation, for example, can promote a single electron from a bonding orbital to an antibonding orbital in the basic case of a hydrogen diatomic molecule. The link between the two hydrogen atoms is weakened as a result of this promotion, which can lead to photodissociation—the breaking of a chemical bond as a result of light.
The relationship between a metal’s valence electron configuration and the strength of metallic bonding is explained by band theory. These atomic orbitals are close enough in energy that the resulting bands overlap because the valence electrons are not restricted to a single orbital.
Valence band :
It’s made up of electron-filled valence shell orbitals. A sodium valence band, for example, is made up of 3s1 orbitals. 1s2, 2s2, 2p6, 3s1 is the electrical configuration of sodium.
Conduction band :
It is made up of those orbitals in the valence shell or higher empty shell that are not occupied by electrons. As a result, the conduction band’s orbitals are vacant. Let’s use sodium as an example: after orbital 3s, the next orbital 3p is unoccupied, forming a conduction band. In other terms, we can say that the valence band is the highest energy band that is filled. The conduction band is the next possible band in the energy structure that is vacant.
Orbitals of the conduction band are empty :
The valence band, by definition, is the last band to be fully occupied. By definition, the conduction band is the one that is directly above (in energy) the valence band.
Even at 0 kelvin, the conduction band of metals is partially occupied.
The conduction band in semiconductors is empty at 0 kelvin, but depending on the energy splitting between the top of the valence band and the bottom of the conduction band, it can be inhabited at higher temperatures.
Conclusion :
Band theory is a theoretical model in solid-state physics that defines the states of electrons in solid materials that can only have energy values within defined ranges.Due to the lack of a bandgap, metals have a partially filled valence band and a partially filled conduction band. The hypothesis predicts that metals conduct extraordinarily well (both heat and electricity) and is universally recognized. We know that atomic orbitals overlapping generate molecular orbitals.
