Probability Distributions for Atoms and Molecules

The central result of this chapter is the Boltzmann distribution law, which gives probability distributions from the underlying energy levels. We derive this result b bringing together the two main threads from earlier chapters. First, the principles of thermodynamics in Chapters 7-9 describe how to predict the state of equilibrium. Second, Chapter 6 relates a macroscopic property of the equilibrium (the entropy) to a microscopic property, the probability distribution. 

Here s the kind of problem we want to solve. Example 8.2 (page 13.5) describes a two-dimensional model of a four-bead polymer chain that has four open conformations and one compact conformation. In that example, we com- 

Now we derive the probability distribution for any system with known energy level spacings. We do this by combining the definition of entropy, S/k = - S Pi In Pi, with the definition of equilibrium. Our approach follows the dice problems of Chapter 6, but now instead of knowing an average score, we take the average energy of the system. 

---