Calculate the number of ways to arrange energy in an Einstein solid.
(a) Model a system consisting of two atoms (three oscillators each), among which 4 quanta of energy are to be
distributed. Write a program to display a histogram showing the total number of possible microstates of the twoatom system vs. the number of quanta assigned to atom 1. Compare your histogram to the one shown in Figure
12.15 (you should get the same distribution).
(b) Model a system consisting of two solid blocks, block 1 containing 300 oscillators and block 2 containing 200
oscillators. Find the possible distributions of 100 quanta among these blocks, and plot number of microstates vs.
number of quanta assigned to block 1. Compare your histogram to the one shown in Figure 12.21. Determine the
distribution of quanta for which the probability is half as large as the most probable 60-40 distribution.
(c) Do a series of calculations distributing 100 quanta between two blocks whose total number of oscillators is 500, but
whose relative number of atoms varies. For example, consider equal numbers of oscillators, and ratios of 2:1, 5:1,
and so on. Describe your observations.