Question

According to classical free electron theory:
A) There is no interaction between conduction and the interaction of electrons.
B) The interaction of free electrons with ion cores is negligible.
C) The free electron find uniform electric field of positive ions and that of electrons in metal
D) All the above

Answer 1

Hint: To answer this question, we should know what classical free electron theory is, who gave it and what the points it contains. We should also know all the assumptions it takes and if it’s used or not.

Complete step by step solution:
The classical free electron theory was proposed by Drude and Lorentz in 1900. 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.
2. The free electrons of the atoms move in a random direction. While doing so they collide with either positive ions fixed to the lattice or the other free electrons of the atom. But there is no loss of energy as all the collisions are elastic in nature.
3. The momentum of free electrons of the atoms obeys the laws of the classical kinetic theory of gases.
4. The velocity with which the free electrons are moving in metal also obeys classical Maxwell-Boltzmann distribution of velocities.
5. When the electric field is applied to the metal, the free electrons are accelerated in the direction opposite to the direction of the applied electric field.
6. There is no mutual repulsion among the electrons. So that they move in all directions with all possible velocities.
7. In the absence of the field, the energy associated with an electron
$\dfrac{3}{2}kT = \dfrac{1}{2}m{v^2}$
Where $T$ is the temperature, $k$ is the Boltzmann constant, $m$ is the mass of the electron and $v$ is the velocity.

Hence we can conclude that option (A) is the correct answer.

Note: This classical theory has both positive points and negative points. Some of them are: It verifies ohm’s law, the electrical conductivity of metals, and the thermal conductivity of metals. But it fails to explain the photoelectric effect, Compton Effect, and black body radiation.