The transport of electrons and positive holes

The electrical properties of solids are categorized into classes of conductivity dirough Ohm s law which states a relationship between conductivity a, cunent density J and applied potential E 

If the average time between collisions is 2r then the relaxation time is defined by 

The temperature coefficients of conductivity of metallic systems are characteristically negative because of the increased scattering of the electrons brought about by the increasing amplitude of vibration of the ion cores. 

When electrons traverse an alloy rather than a pure metal, the scattering of electrons is different at the ion core of each chemical species and so the conductivity reflects a mixture of the effects due to each species. In a series of copper alloys it was found that the resistance, which is the reciprocal of the conductivity, is a parabolic function of the concentration of the major element 

The behaviour of electrons in metals shows the translational properties of quantum particles having quantized energy levels. These cannot be approximated to the continuous distribution describing particles in a gas because of the much smaller mass of the electron when compared with atoms. If one gram-atom of a metal is contained in a cube of length L, the valence electrons have quantum wavelengths, X, described by the de Broglie equation 

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