prob set 6 - PHYS 271 Problem Set 6 Due Tuesday Apr 14 2009...

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PHYS 271: Problem Set 6 Due Tuesday, Apr. 14, 2009 at the start of class. 1. Imagine we have a chunk of metal whose density of states is given by g ( E ) = 10 23 × E ( E 0 ) 2 where E is in eV, and E 0 = 10 eV. (a) If our chunk of metal is at zero temperature (in degrees Kelvin), and has 10 23 electrons in it, find the Fermi energy E F of the metal. Do not worry about spin (i.e. assume that each energy level can have at most one electron in it). (b) Suppose now that we are at some non-zero temperature T . Also assume that the Fermi energy is the same as what you found in part (a). Let p be the probability that an energy level with E = 1 . 01 E F is occupied. What must T be to have p = 0 . 01? Give your answer in degrees Kelvin. (c) Suppose we are at the same temerpature T as part (b). How many electrons do we expect to find in energy levels with energies between E = E F and E = E F + 10 - 2 k B T ? Note that you DO NOT need to do any integrals here! Use the same value of E F as you found in part (a).
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