The free electron theory is based on the following assumptions. The valence electrons of atoms are free to move about the whole volume of the metal, like the molecules of a perfect gas in a container. The free electrons move in random direction and collide with either positive ions fixed to the lattice or the other free electrons. All the collisions are elastic in nature i.e., there is no loss of energy. The momentum of free electrons obeys the laws of the classical kinetic theory of gases. The electron velocities in a metal obey classical Maxwell-Boltzmann distribution of velocities. When the electric field is applied to the metal, the free electrons are accelerated in the direction opposite to the direction of applied electric field. The mutual repulsion among the electrons is ignored, so that they move in all the directions with all possible velocities. The movement of free electrons inside a metal is equivalent to the motion of free electrons in a potential well.
