write N(E) = CE1/2, where Cis a constant of proportionality. The occupation probability is one for energies below the Fermi energy and zero for energies above. Thus, ECnEdECnEFEFavg==z3252025//. Now 1/23/2002()().3FEFCnNEPEdECEdEE∞=∫∫We substitute this expression into the formula for the average energy and obtain ECECEEFFFavg=FHGIKJFHGIKJ=253235//.21. The average energy of the conduction electrons is given by
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