Classical and Quantum Conductivity - Conductivity - Flaws in Classical Conductivity

Flaws in Classical Conductivity

While the classical understanding of conduction is useful in constructing Ohm’s law and providing an understanding of the motion of electrons, there are a number of inherent flaws in this theory. Firstly, the above stated equation for resistivity will give a value that is about seven times the measured value of resistivity at a temperature of 300 K. Furthermore, it can be shown by experiment that resistivity has a linear relationship with temperature, while the resistivity in accordance to the classical theory is reliant on the value , which is related to the square root of temperature. There are some flaws from a statistical perspective as well. Applying Boltzmann statistics and the Maxwell distribution of speeds, the electrons that are viewed as particles will give an average kinetic energy of (3/2)kT. The molar heat capacity of a metal is expected to be (3/2)R greater than that of insulators, which has a heat capacity of 3R. In other words, it is expected that the molar heat capacity of metals will be (9/2)R. However, this is not observed. The experimentally determined molar heat capacity of metals is close to 3R. One last problem, (which will actually be key in the quantum solutions) is that it is known that electrons share wave-like properties as well, and the classical theory makes no mention of such properties.