The free electron theory of metals Motion

Next consider the motion of these electrons. It was already mentioned that in addition to their density, metallic electrons are characterized, at this level of theory, by a relaxation time t. In the Drude theory this enters via a simple friction force by assuming that under a given force f (i) the electron moves according to 

This implies that at steady state under a constant force the electron moves with a constant speed v = rf. Using f = — e where is the electric field and — e is the electron charge, and the expression for the electric current density in terms of the electron density zi, charge —e and speed v. 

The coefficient that relates the current density to the electric field is the conductiv-ity cr. We found 

The conductivity obtained from the Diaide model is seen to be proportional to the electron density and to the relaxation time, and inversely proportional to the electron mass. 

Note that the conductivity cr has the dimensionality of inverse time. The Drude model is characterized by two time parameters r, that can be thought of as the time between collision suffered by the electron, and cr. Typical values of metallic resistivities are in the range of 10 - Qcm, that is, cr = lO fQcm) = 10 s L Using this in (4.69) together n lO cm , e 4.8 x 10 ° esu and m 9 X 10 g leads to r of the order 10 s. Several points should be made  

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