All answers in this question must be accurate to 0.1%. For this set of related questions, consider two spin 1/2 paramagnets, interacting with each other. Recall that a this means that each atom has two energy states available to it: a ground state, with energy zero, and an excited state, with energy 6. Let para magnet A have NA = 10 atoms and paramag net B have NB 2 7 atoms. Let the two paramagnets together have energy E = 86. Make a table similar to that in figure 2.4 of Schroeder (use a computer if you find it tedious), and answer the following questions: (a) lfthe two paramagnets are allowed to reach thermal equilibrium, how many 6 units of energy are in paramagnet A most often? l 5 I (b) Denote the number of units of energy you determined in part (a) with Q. At thermal equilibrium, what fraction of time does paramagnet A spend having (11, Q or 0+1 units of energy? 0.3628 R (c) What fraction of time does paramagnet B spend having no energy units at all? l 0001851 I (d) What is the average energy in paramagnet A, in units of 6? l 4.706 I Notice that questions (a) and (d) are not asking for the same quantity. 2.3 Interacting Systems QB total = QAQB 100 9 B 6 28 28 80- 21 63 15 90 60 total 10 100 40- OHNO A O 90 H O O 21 63 20- 28 28 462 = (6+6-1) 0 1 2 3 4 5 6 6 Figure 2.4. Macrostates and multiplicities of a system of two Einstein solids, each containing three oscillators, sharing a total of six units of energy