This theory has some assumptions; they are: The valence electrons of metallic atoms are free to move in the spaces between ions from one place to another place within the metallic specimen similar to gaseous molecules so that these electrons are called free electron gas.
What are the salient features of the free electron gas model?
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.
What is free electron model theory?
A free electron model is the simplest way to represent the electronic structure of metals . ... According to this model, the valence electrons of the constituent atoms of the crystal become conduction electrons and travel freely throughout the crystal.
What are the basic assumptions of the Drude model?
The simplest analysis of the Drude model assumes that electric field E is both uniform and constant, and that the thermal velocity of electrons is sufficiently high such that they accumulate only an infinitesimal amount of momentum dp between collisions , which occur on average every τ seconds.
What are the assumptions of free electron model?
The ‘free electron’ model of metals assumes that the conduction electrons of the valence band are not confined to individual atoms . They are distributed through the metal like an electron gas. Interactions of the electrons with the core metal ions and with each other are neglected.
What is a free electron?
1 : an electron within a conducting substance (as a metal) but not permanently attached to any atom .
What is the energy of a free electron?
The free electron kinetic energy of Equation (1.37) is obtained from the plane wave solution φ = e − ik . r of the Schrödinger equation, (1.45) with the potential V(r) set equal to zero. When a potential, such as that shown in Fig.
What is the role of free electron?
The electrons which are not attached to the nucleus of a atom and free to move when external energy is applied are called free electrons. ... The moving free electrons will transmit electric current from one point to other . Materials which contain free electrons will conduct electric current.
What is electron gas theory?
This theory was proposed by Drude and extended by Loren (1932). ... According to this theory, each atom in a metal crystal loses all of its valence electrons . These valence electrons from a pool or a gas. The positively charged metal ions are believed to be held together by electron pool or gas.
What is electron gas model?
Free-electron model of metals, in solid-state physics, representation of a metallic solid as a container filled with a gas composed of free electrons (i.e., those responsible for high electrical and thermal conductivity). ... The free-electron model was first proposed by the Dutch physicist Hendrik A.
Why is potential energy of electron is taken as zero in free electron theory?
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.
Which of the following is true for free electron theory?
Explanation: The free electrons move randomly in all directions . The free electrons collide with each other and also with the lattice Elastically, without loss in energy.
How do you find the free electron?
Free Electron Density in a Metal
will have free electron density n = x10^ /m 3 . will have a number of atoms per unit volume n’ = x10^ /m 3 . The number of atoms per unit volume multiplied by the number of free electrons per atom should agree with the free electron density above.
What is failure of Drude model?
The Drude model cannot explain the conductivity of alloys . Even small impurities can drastically decrease the conductivity of metals in a way which is not predicted by the Drude model. From a classical mechanics perspective, the electrons should contribute greatly to the heat capacity of metals.
What is Lorentz theory?
Lorentz- Drude suggested that conductors such as metals contain a great number of free electrons . The positive ions are fixed at their sites. ... In an open circuit, the negative ions (electrons) move at random in the lattice. When the lattice is closed the electrons will be arranged in orderly movement.
What are the failure of Drude Lorentz free electron theory?
The Drude model does have its limitations such as its failure to correctly account for the temperature dependence of resisitivity in metals , but it gives a good enough classical description of electrical conduction in metals which leads to Ohm’s law and shows that resistivity in a metal can be explained by the motion ...
