Electron Theory of Metals. Energy Distribution

In the preceding section we spoke of an electron gas , and pictured it to ourselves as a definite number n per cm. ) of electrons, moving freely, without mutual disturbance. Such a case is of course unrealizable, since in virtue of their electric charge the electrons will always act upon each other however, to a first approximation we can neglect this disturbing action, owing to the neutralizing effect of the positive ions. 

The Bolution of this difficulty is due to Pauli and Sommerfeld (1927), who pointed out that the laws of classical statistics ought not to be applied to the electron gas within a metal, since it is bound to behave as a degenerate gas. Thus, since the mass of the electron is 1840 times smaller than that of the hydrogen atom, it follows that, at room temperature T = 300°) and an electronic density oi n 3T0 , corresponding to a gas density at a pressure of 1 atmosphere, the value of the degeneracy parameter for the electron is 

We therefore obtain the following distribution curve for the electrons 

The distribution function, which is approximately valid for large values of A, i.e. for low temperatures, is then 

As the temperature increases, the electrons are gradually raised into higher states but the change in the electronic distribution will at first only take effect at the place where the Fermi function falls 

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