PHYS 330 Homework
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   Homework #10: Due Friday October 31 by 5:30pm.
  1. problem 6.13
  2. Consider a hypothetical atom with just two energy states: A doubly-degenerate ground state of energy=0eV, and a four-fold-degenerate excited state with energy=0.500eV. Determine the value of the partition function for this system for the following temperatures: (a) in the limit that T→0K, (b) 300K, (c) 3x104K, (d) 3x105K, (e) 3x106K, (f) 3x107K, and (g) in the limit the T→infinity. This last one for T→infinity should be an exact number. Make a plot of your results--use a logarithmic scale for the temperature (i.e. log(T) on the x-axis would have the values 0, 1, 2,...7, 8).
  3. Consider a hypothetical atom with just two energy states: A doubly-degenerate ground state of energy=0eV, and a four-fold-degenerate excited state with energy=0.500eV. Find the expression for the heat capacity "C" of this system, recalling that C=d<E>/dT. You can do this by hand, or by using Mathematica (or Maple). Show your work, or turn in the computer printout. If you use Mathematica , etc., then turn in your printout with this problem but I have to see all the steps. In the end, evaluate this heat capacity at 4,000K.
  4. Consider an electron in a computer chip. This electron is contained in a 1-d "box" (i.e. a 1-d wire) whose length is 15nm. Let the temperature (a kinetic temperature, not the "real/heat" temperature) be 1,000K. (a) Find the approximate maximum number of quantum states in which this electron may be. (b) Find the energy of the lowest three energy states in this arrangement.
  5. Consider an electron trapped in a 2-d "box" with sides of length L=2.0nm. Sketch the following probability densities (probability clouds like I did in class) for the following quantum values for (nx, ny): (a) (1,1) (b) (2,3) (c) (4,2). Note that you should be able to do this for any values for each 'n.'
   That's all for homework #10.