Unformatted text preview: EE138: Homework Assignment #3 U HOMEWORK DUE: 11/04/2009 (in lecture) HOMEWORK QUIZ: 11/06/2009 (in lecture) Problem #1: (a) Calculate the wavelength of the electromagnetic waves needed to excite a hydrogen atom from the 1s into the 2s state. (b) Calculate the energies of valence electrons of He, Be, and Mg predicted by the following Z2
equation: E n 13.6 2 . n
(c) Determine the average radius of an electron in the ground state of the hydrogen atom. Problem #2: (a) What are the three primary bond types? Give an example of a material with each bond type and give a brief description (1‐2 sentences) of each bond type. (b) Describe the energy for (1) a free electron, (2) a strongly bound electron, and (3) an electron in a periodic potential. Why do we get these different band schemes? Problem #4: (a) Use a computer to plot the Fermi‐Dirac distribution for Cu at T = 0, T = 300 K, and T = 1200 K. Use the Fermi energy for Cu found in Table 6.1 in S & W. (b) What is the probability a state is filled at E = 7.11 eV for each temperature you plotted in part (a)? (c) What is the probability a state is empty at E = 7.11 eV for each temperature you plotted in part (a)? Problem #5: (a) What is the definition of the Fermi energy, EF? (b) Calculate the Fermi level for conduction electrons in copper. Assume one conduction electron per atom. The atomic weight of copper is 63.5 and its density is 9.4 x 103 kg m‐3. Use mo=m*. (c) At what temperature can we expect a 10% probability that electrons in silver have an energy which is 1% about the Fermi energy? (EF = 5.51 eV from Table 6.1 in S & W) Problem #6: (a) What is the minimum frequency of electromagnetic radiation capable of generating photoelectrons from the bottom of the 3s energy band in Na metal? (Use Tables 6.1 & 6.2 in S &W.) (b) If you generate photoelectrons from Na metal with ultraviolet radiation 100 nm wavelength, what will be the kinetic energy of the photoelectrons from the 3s band? U U U U U Problem #7: Band X U Energy, E Band Y
Band Z Wave number, k (a) What is the group velocity of an electron in Band X at (1) k = 0, (2) k = ‐/a, and (3) k = /a for the energy band shown? (b) Sketch the effective mass for Band X. (c) Does Band Y or Band Z have a larger effective mass? How do you know? ...
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