Physics 301 Problem Set 5 - Princeton University

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Physics 301 Problem Set 5. The reading assignment is Chapter 6. We will not ask you anything based on 6.10 but in it Reif introduces the concept of ”information ...
Physics 301 Problem Set 5 The reading assignment is Chapter 6. We will not ask you anything based on 6.10 but in it Reif introduces the concept of ”information,” a part of the branch of mathematics called ”information theory.” The section may be of interest. Problem 1. (10 pts) At very high temperatures (e.g., the early universe) the proton and neutron can be thought of as two different states of the same particle called a ”nucleon.” The protons and neutrons can easily be converted from one to another by interacting with photons, electrons, and neutrinos which are abundant and in equilibrium with the nucleons at these early times. The neutron’s mass exceeds the proton’s by 2.3 × 10−30 kg. When the universe was 1011 K, what fraction of the nucleons were neutrons? Problem 2. (10 pts) A zipper has N links each of which can be closed with energy of zero, or open with an energy of . The zipper can only unzip from the left. Thus, if link s is open so must be all links to its left (0,1,2,...s − 1). This is a very simplified model for the unwinding of DNA. It comes from Kittel, Am.J.Phy, 37,917 (1969). Reif’s Appendix A.1 may be helpful. a) Show that the partition function is Z=

1 − e−(N +1)/kT . 1 − e−/kT

(1)

b) In the limit that  >> kT find the average number of open links. Problem 3. (10 pts) Reif 6.1 Problem 4. (10 pts) Reif 6.6 Problem 5. (10 pts) Reif 6.7 Problem 6. (10 pts) Reif 6.9 Problem 7. (10 pts) Reif 6.10 Problem 8. (20 pts) Reif 6.11. This is called the Lennard-Jones potential. We will return to it in Chapter 10.

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