What are the assumptions of free electron theory?
Assumptions of Classical free-electron theory: All metals contain large number of free electrons which move freely through the positive ionic core of the metals. Since these free electrons causes conduction in metal under the application of electrical field, they are called as conduction electrons.
What are the salient features of classical free electron theory?
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 are the limitations of free electron theory?
1) It fails to explain the electrical conductivity of semiconductors and insulators. temperature. 3) It fails to explain the concept of specific heat of metals. 4) It fails to explain the mean free path of the electrons.
What are the assumption of free electron theory of metals explain electrical conductivity using free electron theory of metals?
The classical free electron theory was introduced by P. Drude in 1900 and developed by Lorentz in 1909 to explain electrical conduction in metals. This theory has some assumptions; they are: There is no interaction between these conduction electrons. The interaction of free electrons with ion cores is negligible.
What are the failures of classical free electron theory?
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 are the assumptions of free electron theory of metals explain electrical conductivity using free electron theory of metals?
What is the energy of 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.
What are the assumptions of quantum free electron theory of metals?
Assumptions (Postulates) of Quantum free electron theory 1. In a metal the available free electrons are fully responsible for electrical conduction. 2. The electrons move in a constant potential inside the metal.
What are the merits and demerits of quantum free electron theory?
Advantages of Quantum free electron theory 1. This theory fails to distinguish between metal, semiconductor and Insulator 2. It also fails to explain the positive value of Hall Co-efficient. 3.
What are the failures 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 are the assumptions in the free electron model?
6.1 Basic Assumptions In the free electron model, we assume that the valence electrons can be treated as free, or at least moving in a region constant potential, and non-interacting. We’ll examine the assumption of a constant po- tential first, and try to justify the neglect of interactions later. 2
What was the first theory of free electrons?
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. 2.
When did Drude and Lorentz develop the free electron theory?
The classical free electron theory Drude and Lorentz proposed this theory in 1900. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. The quantum free electron theory Somerfield developed this theory in 1928. According to this theory the free electrons obey quantum laws.
How are free electrons in a periodic field?
electrons obey quantum laws. According to this theory the free electrons are moving in a constant potential. The zone theory Bloch stated this theory in 1928. According to this theory, the free electrons move in a periodic field provided by the lattice. According to this theory the free electrons are moving in a constant potential. 2.