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Discussion3 - 1 Consider the Fermi-Dirac Distribution what...

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1) Consider the Fermi-Dirac Distribution, what is the probability of finding an electron with: (a) an energy that is 4% higher than the Fermi energy at 0K? (b) an energy that is 4% lower than the Fermi energy at 0K? (c) an energy that is 4% higher than the Fermi energy at 298K? (d) an energy that is 4% lower than the Fermi energy at 298K? (e) an energy that is 4% higher than the Fermi energy at 1000K? (f) an energy that is 4% lower than the Fermi energy at 1000K? For each case consider than the Fermi energy is 5 eV. Draw a graph of energy vs. the Fermi-Dirac Distribution for the three temperatures indicated above and demark the energies that are 4% lower/higher than the Fermi energy, as well as the corresponding probabilities. Solution: Using the Fermi-Dirac Distribution ( 29 1 exp 1 + - = T k E E E F B F Probability at Temperature (K) E 4% higher E 4% lower 0 0 1 298 0.0004142 7 0.999585 7 1000 0.0893991 6 0.910600 8 Ef (eV) 5 E 4% higher (eV) 5.2 E 5% lower (eV) 4.8 F(E) E 0 E F =5eV 1 T=0K T=1000K T=298K
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2) Consider a monovalent metal such as gold and a divalent metal such as zinc.
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