Quantum Theory of Electrons in Metals

Quantum Theory Of Electrons In Metals

The drawbacks of classical theory can be rectified using quantum theory.

In classical theory the properties of metals such as electrical and thermal conductivities are well explained on the assumption that the electrons in the metal freely moves like the particles of a gas and hence called "free-electron gas."

According to classical theory, the particles (electrons) of a gas at zero kelvin will have zero kinetic energy ( Since E=3/2 K_BT ) and hence all the particles are found to be in rest. But according to quantum theory when all the particles are at rest, all of them should be filled only in the ground state energy level, which is impossible and is controversial to the pauli's exclusion principle.

Thus inorder to fill the electrons in a given energy level, we should know

the following.

(i) Energy distribution of electrons

(ii) Number of available energy states

(iii) Number of filled energy states

(iv) Probability of filling an electron in a given energy state, etc.