\"Xe is an isotope of Xenon with a nuclear spin of 'f: . When 1\"Xe is in an external magnetic field. an energy dilTerence arises between the state where the nuclear spin is aligned with the magnetic field and the state where nuclear the spin is anti-aligned to the eld. I. Let the lower energy state be denoted as \"-\" with energy E_ = 0 and the higher energy state be denoted as \"+\" with energy E4. = p8 where it is the magnetic moment of \"'Xe. and B is the strength of the external magnetic field. a) write an expression for the molecular partition function associated with the two different spin states. 95pm in a magnetic eld with strength 3. b) what is the limit of 4m: as the temperature approaches 0 K'.' c) what is the limit of qwin as the temperature approaches +00? d) Write an expression for p... the probability ofnding a I\"Xe in the higher energy. "".+ stale. e) For Xe, u = 3.94 x 10-27 Joules/Tesla. Calculate qspin when the temperature is 200K, and the magnetic field is 10 Tesla. 2. Consider N atoms of 12"Xe contained in a volume, V, in the presence of a magnetic field, B. a) Assuming that Xe is an ideal gas, write the expression for the translational molecular partition function, qtrans . You can take this directly from your notes or from the textbook. b) The mass of 129Xe is 128.8 amu, and I amu is 1.661x10-27 kg. What is the value of the translational partition function at 200 K for 12"Xe in a 100 L container?3. Now combine the results from 1 and 2. a. Using qmm, from 2a] and qwmfrom lo). write an expression for the total molecular partition function. gram. b. Using your answcr from 3:1} write an expression for the canonical partition function. G. for N molecules of "'Xc. in a volume. V. at temperature T. with magnetic eld B. c. Using your result front 3b) write an expression for the system energy d. What is the system energy at 300K, with a magnetic field of 10 Tesla, 1 mol of 129Xe and 10 L volume? e. What is the system energy at 300 K when the magnetic field is zero Tesla? f. Based on a comparison between 3d) and 3e), comment on the importance of considering the Earth's magnetic field (3 x 10" Tesla) when computing the total energy of a Room Temperature collection of 129Xe