Note: This homework has several superscripts and subscripts out of necessity, so you'll need to print this out on a printer that shows this. Or, be sure to correct your own printout if you do this on a printer that has trouble with such things.

1. problem 6.5
2. problem 6.7. In this problem, referring to Figure 6.2, you should see that the energy levels are given by the standard Bohr approximation, E_n=(-)13.6eV/n². Note the degeneracies here are g₁=2*1=2, g₂=2*4=8 and g₃=2*9=18 (1+3+5) for n=1 (ground state), 2 (first excited) and 3 (second excited), respectively. Just as I discussed in class.

That's all for homework #6.

I want to point out the importance of the units thing with this statistical mechanics work. You're used to Boltzmann's constant k=1.38066x10^-23 J/K. But you get things in units of electron volts by dividing by the charge of the electron, or e=1.60218x10^-19 Coulombs, so that k=8.61738x10^-5 eV/K. These constants will be on the front of the exam, but these should also be in the front of your minds anyway. They're on the front of the exam since their exact numbers are things you'd look up in real situations.

I also want to emphasize that in statistical mechanics the quantity "kT" is the amount of thermal energy you have with which to make things just from one energy state to another. But that exponential Boltzmann factor disfavors the higher energy states quite thoroughly. Thus the partition function "Z" is so important, which is why I spent two days in class working through two big examples with it.

Go back to Dr. Herman's homepage.