Test02 - Test 2(Thursday 21 April Problem 1 Admixing Al to...

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Test # 2 (Thursday, 21 April) Problem # 1 Admixing Al to Ag creates an Ag 1- x Al x alloy (in which Al atoms substitute for Ag atoms) and leads to an increase of the Fermi energy. Using a free electron model and assuming that Al is trivalent while Ag is monovalent calculate the relative concentration, x , of Al atoms which is required to increase the Fermi energy by 1eV. Take into account that the Ag crystal has electron concentration n = 5.85 10 22 cm -3 . Problem # 2 Suppose that the electronic structure of a solid that represents a two-dimensional square lattice of divalent atoms can be described using a nearly free electron model with a weak crystal potential such that 2 2 2 U ma π ⎛⎞ ⎜⎟ ⎝⎠ G = ± , where a is the lattice parameter. Is this solid a metal, an insulator or a semiconductor? Explain why. Problem # 3 Both free electrons and phonons can be treated in terms of a gas of non-interacting particles. Why, then, the electron heat capacity at low temperatures is proportional to T , whereas
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