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Homework #10: Due Friday October 31 by 5:30pm.
That's all for homework #10.
- problem 6.13
- 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).
- 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.
- 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.
- 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.'