the advantages and the drawbacks of the quantum and classical free electron theory
Answers
Answer:the major advantage is cost. Normally, electrons can be quite expensive. Therefore, the ability to obtain free electrons substantially reduces laboratory costs. The disadvantage is that free electrons are often inferior in terms of quality compared to electrons purchased at market rates.
Explanation:
The main kinds of bonds are covalent, ionic, and metallic. Whereas the electrons in the first two tend to be locked to specific atoms, metallic bonds form by having a cloud of electrons freely wandering around a solid comprised of positive ions. The electrons behave like a gas whose particles have mainly kinetic energy away from the boundary and mainly potential energy at the boundary, as with any gas. This picture allowed Lorentz and Drude in 1900 to come up with a theory of thermal and electrical conductivity in metals.
But whereas a classical gas obeys Maxwell-Boltzmann statistics, free electrons obey Fermi-Dirac statistics because they are fermions. As a consequence of Heisenberg uncertainty the distribution of energies is limited by the coarseness of phase space, with cells of size h^3 where h is Planck’s constant. Hence the advantages of the quantum version of free electron theory as developed by Arnold Sommerfeld in 1927 are more accurate modeling of conduction and the many other advantages listed at this article.
The disadvantages include wrong temperature dependence at high temperatures due to ion motion and phonon scattering, lack of dependence of conductivity on any crystal structure present in the metal (it may not be isotropic), inadequate account of semiconductors and dielectrics, no explanation of colors of metals (gold is yellow, copper is more brown