Plot the Fermi-Dirac probability of occupation function fFD(E) for T = 0, 10, 100, 200, 300 and 400K.
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- Plot the Fermi-Dirac probability of occupation function fFD(E) for T = 0, 10, 100, 200, 300 and 400K.
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- Suppose that ak > 0 for all k e N and E ak < 0. For each of the following, prove that the given series converges. ak ( a ) ΣΕΙ 1+ k3ak (b) Lk=1 1+ ak Vak (c) Ek=1 k < 0o.For 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval dE around a given energy E as g(E): = dn dE 3 (2m₂)2V 1 E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. From the density of states, what is the relation between the total electron states N below a given energy E? Use this result to show that the Fermi energy EF is given by - - 2010 (307² M)³ ħ² 3π²N\3 EF 2me VThe probability of finding an N2 molecule at ambient temperature at 515 m/s is zero. True or False?