It has been developed in three main stages. 1. Classical free electron theory: The first theory was developed by Drude and Lorentz in 1900. According to this theory, metal contains free electrons which are responsible for the electrical conductivity and electrons obey the laws of classical mechanics.
What is free electron theory of solids?
According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a gas in a container. Mutual repulsion between electrons is ignored and hence potential energy is taken as zero. Therefore the total energy of the electron is equal to its kinetic energy.
What is free electron with example?
The particles are close together and in a regular arrangement. Metals atoms have loose electrons in the outer shells, which form a ‘sea’ of delocalised or free negative charge around the close-packed positive ions. These loose electrons are called free electrons. They can move freely throughout the metallic structure.
What is the formula of the free electron?
Free Electron Theory of Metals where E is the electron energy. This gives the familiar parabolic E–k dispersion relation (see Figure 1), E = ħ2k2/2m (with electron momentum p = ħk).
Who gave free electron theory?
1. A classical free electron theory is a macroscopic theory proposed by Paul Drude in 1900. After the discovery of electron by JJ Thomson, this theory was elaborated by Lorentz in 1909. Hence this theory is also known as Drude & Lorentz.
What is free electron theory What are its main assumptions?
This theory said that metals with free electrons obey the laws of classical mechanics. Assumptions used in classical free electron theory. 1. The valence electrons contained in an atom, are free to move about the whole volume of the metal, as the molecules of a perfect gas move in a container.
What are the limitations of free electron model?
Drawbacks of classical free electron theory 1) It fails to explain the electric specific heat and the specific heat capacity of metals. 2) It fails to explain superconducting properties of metals. 3) It fails to explain new phenomena like photo-electric effect, Compton effect, Black body radiation, etc.
What is the difference between free electron theory and band theory of solids?
So, the basic difference between these two theory is that the band theory differentiate between the conductors, semiconductors and insulators, whereas , free electron theory only tell us about how conduction is occur in conductors.
What is free electron theory in semiconductor?
The classical free electron theory was proposed by Drude and Lorentz. According to this theory the electrons are moving freely and randomly moving in the entire volume of the metal like gas atoms in the gas container. When an electric field is applied the free electrons gets accelerated.
Why is called free electrons?
These free electrons are named so because they move around freely without being attached to the nucleus. These electrons do not experience any electromagnetic force. These free electrons move through the substance and are responsible for carrying electric current and heat.
What is the difference between electrons and free electrons?
The outermost shell of any atom is called the valence shell and the electrons that reside in the valence shell are called valence electrons. When the valence electrons in any atom gain sufficient energy from some outside force, they can break away from the parent atom and become what are called a free electrons.
What is the speed of a free electron?
Average moving velocity of free electrons is only 1.6e-7 m per second, which is 0.0006 m per hour, and it’s far slow than tortoise wake. If electric current carries electricity and electric current is electron flow, moving velocity of electricity is about the same as walking speed of human.
What is energy of free electron?
For free electrons, there is no potential energy (inside the box), so we can use equation (6.1) to describe the system. For this problem we let V ∞ at the walls of the box. As such, we can set 0=L=0 .
Do free electrons have energy?
Most free electrons are formed with low kinetic energy, and they simply diffuse through the gas, taking part in the random thermal motion of all the atoms. Some free electrons are formed with enough kinetic energy to cause additional excitation and ionization.
What is free electron Fermi gas?
An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi-Dirac statistics.
What is the role of conductivity in free electron theory?
These electrons are responsible for conduction of electricity through metals. Since the conduction electrons move in a uniform electrostatic field of ion cores, their potential energy remains constant and is normally taken as zero. Thus the total energy of a conduction electron is equal to its kinetic energy.
What happens to a free electron?
The flow of free electrons in a material is called an electric current. The moving free electrons will transmit electric current from one point to other. Materials which contain free electrons will conduct electric current. Materials which does not contain free electrons does not conduct electric current.
What is meant by Fermi factor?
Under thermal equilibrium, the distribution of electrons among various energy levels is given by statistical function f(E). The function f(E) is called the Fermi factor and this gives the probability of occupation of a given energy level under thermal equilibrium.
What is the band theory of solids?
band theory, in solid-state physics, theoretical model describing the states of electrons, in solid materials, that can have values of energy only within certain specific ranges. The behaviour of an electron in a solid (and hence its energy) is related to the behaviour of all other particles around it.
Who discovered band theory?
Band Theory was developed with some help from the knowledge gained during the quantum revolution in science. In 1928, Felix Bloch had the idea to take the quantum theory and apply it to solids. In 1927, Walter Heitler and Fritz London discovered bands- very closely spaced orbitals with not much difference in energy.
How many types of energy bands are there in solids?
Valence Bands, Conduction bands and forbidden bands are the three important energy bands in solids.
Which element has most free electrons?
Metallic materials like copper, silver and aluminium have plenty of free electrons.
Are free electrons in any conductor?
Materials with high electron mobility (many free electrons) are called conductors, while materials with low electron mobility (few or no free electrons) are called insulators.
What is the difference between a hole and a free electron in a semiconductor?
Solution : (i) Electron is a negatively charged particle having charge `=1.6 xx 10^(-19)C`. Hole is a seat having positive charge which is produced when an electron breaks away from a covalent bond in a semiconductor.
What is classical free electron theory of metals?
Classical free electron theory: The first theory was developed by Drude and Lorentz in 1900. According to this theory, metal contains free electrons which are responsible for the electrical conductivity and electrons obey the laws of classical mechanics.