Content Curator
The band theory of solids is a theoretical model that explains how electrons in solid materials can only have energy levels within particular ranges. According to Bohr's atomic spectrum theory, an isolated atom has distinct energy levels, and an electron's energy is determined by the orbit it is revolving in. Isolated atoms, on the other hand, only exist in crystals.
Key Terms: Electrons, Protons, Neutrons, Nucleus, Band theory, Atoms, material, matter, Conductors, Insulators, Semiconductors, Energy Levels, Solid, Molecule, Quantum state, Pauli's exclusion principle
Band Theory of Solids
[Click Here for Sample Questions]
The quantum state that an electron acquires inside a metal solid is described by the band theory of solids. Every molecule has several different energy levels.
- The behavior of electrons within a molecule is well explained by band theory.
- The information gathered during the quantum revolution in physics was used to build Band Theory.
- Felix Bloch applied quantum theory to solids in 1928.
According to Pauli's exclusion principle, electrons are filled in their respective energy orbits in atoms.
- A molecular orbit with two separate energy levels is formed when two atomic orbitals join.
- 1023 stacked lines in a small space would resemble a band in solids.
- As a result, an energy continuum known as energy bands is formed.
- By showing possible energies for an electron in a material, band theory helps to visualize the distinction between conductor, semiconductor, and insulator.
Also Read:
| Chapter Related Topics | ||
|---|---|---|
| Junction Transistor | Difference between npn and pnp transistor | Types of Transistors & its practical application |
| Uses of Transistor | Transistor as switch amplifier | P-n junction |
Energy Bands in Solids
[Click Here for Sample Questions]
There are many energy bands in solids band theory, but the three most essential energy bands in solids are
- Valence Band
- Conduction Band
- Forbidden Band
Valence band
The valence band is an energy band that consists of valence electron energy levels. The valence band is located underneath the conduction band, and its electrons are freely connected to the atom's nucleus.
Conduction band
The conduction band is the energy band that comprises free electron energy levels. External energy must be provided for the valence electrons to be pushed into the conduction band and become free.
Forbidden band
The forbidden band, often known as the forbidden gap, is the energy gap between the valence band and the conduction band. The forbidden gap and the categorization of materials as conductors, semiconductors, and insulators govern the electrical conductivity of a solid.
Classification of Solids Based on Energy Bands
[Click Here for Sample Questions]
On the basis of energy bands solids are classified into three categories
- Conductors
- Insulators
- Semiconductors
Conductors
A solid in which the valence band and the conduction band are partially filled or overlap each other is called Conductors.
- Conductors allow current to flow very easily.
- In conductors, the forbidden energy gap is negligible or almost zero.
Insulators
In insulators, the valence band is completely filled with electrons and the conduction band is empty and both the bands are separated by a forbidden energy gap of about greater than 3 eV.
Semiconductors
Semiconductors are materials in which the forbidden energy gap between the filled valence band and empty conduction band is very small i.e. about 1 eV.
- For silicon, forbidden energy gap, Eg = 1.2 eV at room temperature
- For Germanium, forbidden energy gap, Eg = 0.72 eV at room temperature
- Semiconductors behave as insulators at 0 Kelvin but behave as conductors at room temperature.
Energy Band Inside An Atom
[Click Here for Sample Questions]
The electron configuration of Na is known to be 1s2 2s2 2p6 3s1. Below are the energy bands for the 1s, 2s, 2p, and 3p. The valence band is in the upper band, i.e. 3s with electrons, while the conduction band is at the energy level above it, with no electrons. We can see that there is no prohibited energy gap in the conductor here.
Energy Levels Inside A Molecule Made Up Of Two Atoms
[Click Here for Sample Questions]
What happens when two sodium atoms come dangerously near to creating a molecule? Each atom can no longer have the configuration that it had previously. If they do, Pauli's exclusion principle will be broken, and they will wind up with many electrons with the same energy levels.
What happens to this system when two atoms approach very near one other? Their separate energy bands will overlap and convert into what we call Molecular orbit, which is the solution. Individual Sodium atoms' 1s orbits unite to produce the 1s molecular orbital. The molecular orbit has two distinct energy levels because two atomic orbitals overlap. A bonding orbital is the lower energy level, and an anti-bonding orbital is the higher energy level. This will happen for every orbit.
Energy Levels Inside A Molecule Made Up Of Three Atoms
[Click Here for Sample Questions]
Consider what happens if we add a third sodium atom to the equation. That is, according to the idea we just studied. Three atomic orbitals will overlap here, resulting in a single molecular orbital with three distinct energy levels. Three energy levels will be inherited by each molecule orbital here. The more atoms we add, the higher energy levels the molecular orbit will have in general.
Energy Levels Inside A Solid Made Up Of Avogadro Number Of Atoms
[Click Here for Sample Questions]
Each molecular orbital of this solid will now have 1023 distinct energy levels if we have a whole solid comprised of sodium with something like 1023 atoms packed together.
- Consider sketching the 1s orbital of a Sodium solid block, drawing the lower and higher energy levels in between, and stacking the 1023 energy levels in between!
- Individual energy levels will no longer be discernible due to the small gaps.
- As a result, it's easier to conceive of it in terms of continuous energy or energy continuity.
- When we look at them in this way, we may call them an energy band rather than a molecular orbit.
Energy Levels Inside A Solid Made Up Of N-Number Of Atoms
[Click Here for Sample Questions]
In general, if there are n atoms in each energy band, there will be n distinct energy levels.
- The molecular orbitals are referred to as energy bands in a system with n atoms.
- Every single 1s and 2s orbital may hold two electrons.
- As a result, a 1s and 2s energy band may fit a total of 2n electrons.
- A single 2p level can accommodate 6 electrons, hence a 2p energy band can accommodate 6n electrons, and so on.
Energy Levels Inside Material Of the Different States Of The Matter
[Click Here for Sample Questions]
If there is a single atom or if there is gas. Atoms in the gas are far apart/infinitely far apart, hence we may treat them as single atoms.
- Every atom has a different energy level, therefore an electron must jump from one to the next since there is no continuous energy available (It is similar to steps).
- As atoms get closer to one another and finally form a solid, an energy continuum forms, which we call bands.
- The available energy levels inside the bands are constant.
- As a result, it's no surprise that this theory's name is "The Band Theory of Solids."
Also Read:
Things to Remember
- The band theory of solids describes the quantum state that an electron achieves inside a metal solid.
- The valence band is a band of energy made up of valence electron energy levels.
- An energy continuum, which we call bands, emerges when atoms grow closer to one another and eventually form a solid.
- Inside the bands, the available energy levels remain constant.
- There will be n different energy levels if each energy band has n atoms.
Sample Questions
Ques. What is the origin of Energy Bands? (2 Marks)
Ans. Assume I bring two Silicon atoms very near together. When two atoms engage with one another, they establish a covalent connection in which they share electrons. As a result, these energy levels combine to create a crystal. Valence electron energy levels are separated into energy bands in this fashion.
Ques. The Band Gap increases with the decrease in the size of the particle. Justify this statement. (2 Marks)
Ans. The energy bands are created by the merger of a large number of atoms and molecules clusters of energy levels.
The number of overlapping orbitals or energy levels diminishes as the particle size decreases, causing the breadth of the bands to narrow, and causing a rise in the energy gap (Forbidden energy gap or Eg) between the valence band and the conduction band.
Ques. On what factors the energy band structure of a solid depends? (2 Marks)
Ans. The width of prohibited energy bands is determined by the atomic constitution as well as the crystalline lattice symmetry. Internal orbit energy levels are closer to nucleus splitting than valence electron energy levels. The energy band splits both stationary and excited energy levels.
Ques. How do energy bands differ in solids? (2 Marks)
Ans. Each electron in an isolated atom has a certain amount of energy associated with it. However, because all atoms in solids are close together, the energy levels of outermost orbit electrons are impacted by the energy levels of nearby atoms.
Ques. Why are bands formed in solid? (2 Marks)
Ans. The energy levels of the valence electrons spread into bands when individual sodium atoms are brought together to create a solid. At the interatomic gap of sodium, these bands significantly overlap.
Ques. How are energy bands filled? (2 Marks)
Ans. The levels of energy bands are produced as a result of the merging of atoms inside materials, rather than single energy levels. An Energy band is a collection of energy levels that are tightly packed together.
Ques. How are energy bands formed? (2 Marks)
Ans. There is just one energy for an electron orbit in a single atom. When two atoms are placed close enough, however, the electrons in the valence shell begin to mingle. As a consequence, an energy band is established, which is the number of permitted energy levels.
Ques. How are solids classified based on the energy bandgap? (2 Marks)
Ans. Based on the distribution of electron energies in each atom, solids can be classed as conductors, insulators, or semiconductors. Energy bands arise in solids as a result of the tiny distances between atoms, the resultant interaction among electrons, and Pauli's exclusion principle.
Ques. How is the bandgap measured? (2 Marks)
Ans. The direct optical band gap of semiconductors is usually determined by extending the linear region of the square of the absorption curve to the x-axis, and a variant of this method developed by Tauc is also extensively employed.
Ques. Why does the bandgap increase with a decrease in size? (2 Marks)
Ans. Due to electron confinement at the nanoscale, the bandgap widens with decreasing size, a phenomenon is known as the "quantum size effect." In basic terms, electrons are restricted, occupying less space than bulk, and so the VBM and CBM potentials are shifted more +ve and -Ve, resulting in a large bandgap.
Ques. What is the relation between bandgap and crystallite size? (2 Marks)
Ans. The relationship between structural and optical characteristics and precursor molarity implies that the bandgap energy and precursor molarity have the greatest effect on the crystallite size of the films. The suggested model's measurement of crystallite size is identical to the experimental data.
Ques. What is the Fermi level in the energy band diagram? (2 Marks)
Ans. The relationship between structural and optical characteristics and precursor molarity implies that the bandgap energy and precursor molarity have the greatest effect on the crystallite size of the films. The suggested model's measurement of crystallite size is identical to the experimental data.
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Also Read:
Comments