9780030839931, Chapter 2, Problem 4P

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Chapter 2, Problem 4P Problem Insensitivity of the Distribution Function to Small Changes in the Total Number of Electrons In deriving the Fermi distribution (page 41) we argued that the probability of a given level being occupied should not change appreciably when the total number of electrons is changed by one. Verify that the Fermi function (2.56) is compatible with this assumption as follows: (a) Show, when « EF, that when the number of electrons changes by one at fixed temperature, the chemical potential changes by 1 = (2.108) where g(ε) is the density of levels. (b) Show, as a consequence of this, that the most the probability of any level being occupied can change by is [Use the free electron evaluation (2.65) of Although temperatures of millidegrees Kelvin can be reached, at which 108, when N is of order 1022 then is still negligibly small. Step-by-step solution There is no solution to this problem yet. Get help from a Chegg subject expert. Ask an expert