NCERT Solutions for Class 12 Chemistry Band Theory of Solids – Unit 1
Chemistry notes for Class 12 : Quantum physics describes the states of electrons in an atom according to the four-fold scheme of quantum numbers. The quantum numbers describe the allowable states electrons may assume in an atom. The analogy of this is, for an example, in the amphitheater, quantum numbers describe how many rows and seats are available. Individual electrons may be described by the combination of quantum numbers, like a spectator in an amphitheater assigned to a particular row and seat.
In a single isolated atom, the electrons in each orbit have definite energy associated with it. But in case of solids all the atoms are close to each other, so the energy levels of outermost orbit electrons are affected by the neighboring atoms. When two single or isolated atoms are brought close to each other, then the outermost orbit electrons of two atoms interact or shared with each other. i.e., the electrons in the outermost orbit of one atom experience an attractive force from the nearest or neighboring atomic nucleus. Due to this, the energies of the electrons will not be in the same level, the energy levels of electrons are changed to a value which is higher or lower than that of the original energy level of the electron. The electrons in same orbit exhibit different energy levels. The grouping of these different energy levels is called energy band.
However, the energy levels of inner orbit electrons are not much affected by the presence of neighboring atoms.
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands).
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Band Theory of Solids: A quantum mechanical model of electrons in solids that predicts certain restricted ranges or the bands, for the energies of these electrons is called as Band Theory of Solids. It is also called as energy band theory of solids. The behavior of an electron in a solid (and hence its energy) is related to the behavior of all other particles around it. This is in direct contrast to the behavior of an electron in free space where it may have any specified energy. The ranges of allowed energies of electrons in a solid are called allowed bands. Certain ranges of energies between two such allowed bands are called forbidden bands—i.e., electrons within the solid may not possess these energies. The band theory accounts for many of the electrical and thermal properties of solids and forms the basis of the technology of solid-state electronics.
A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.
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Important energy bands in solids
There is a number of energy bands in solids but three of them are very important. These three energy bands are important to understand the behavior of solids. These energy bands are
- Valence band
- Conduction band
- Forbidden band or forbidden gap
The energy band which is formed by grouping the range of energy levels of the valence electrons or outermost orbit electrons is called as valence band. Electrons in the valence band have lower energy than the electrons in the conduction band. The electrons present in the valence band are loosely bound to the nucleus of an atom.
The energy band which is formed by grouping the range of energy levels of the free electrons is called a conduction band. Generally, the conduction band is empty, but when external energy has applied the electrons in the valence band jumps into the conduction band and becomes free electrons. Electrons in the conduction band have higher energy than the electrons in the valence band. The conduction band electrons are not bound to the nucleus of an atom.
The energy gap which is present in the valence band and conduction band by separating these two energy bands is called as a forbidden band or forbidden gap.
In solids, electrons cannot stay in the forbidden gap because there is no allowed energy state in this region. The forbidden gap is the major factor in determining the electrical conductivity of a solid. The classification of materials as insulators, conductors and semiconductors are mainly depending upon forbidden gap.
The energy associated with the forbidden band is called energy gap and it is measured in unit electron volt (eV).
1 eV = 1.6 × 10-19 J
The applied external energy in the form of heat or light must be equal to the forbidden gap in order to push an electron from valence band to the conduction band.
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