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Unformatted text preview: Problem 3. For an electron gas in a metal, (a) Prove that the average energy per electron is (3/5) F at T=0 by making a direct calculation of U e (0)/N. (b) Prove that the average speed of the electron at T=0 is (3/4)v F , where the Fermi speed v F is defined by F =(1/2)mv F 2 . Problem 4 . For the metal aluminum (Al), each Al atom contributes three electrons to the conduction band (the free electron gas). The density of aluminum is 2.69x10 3 kgm-3 and its atomic number is 27. (a) Calculate the Fermi energy F . (b) Show that at T=300 K, the chemical potential differs from F by less than 0.01%. (c) Calculate the electronic contribution to the specific heat capacity of aluminum at T=300 K and compare to the contribution of lattice vibrations....
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- Winter '10