A lithium nucleus has four independent spin orientations,

Chapter 6, Problem 11P

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Problem 11P

A lithium nucleus has four independent spin orientations, conventionally labeled by the quantum number m = −3/2, −1/2, 1/ 2, 3/2. In a magnetic field B, the energies of these four states are E = − mµB, where the constant µ, is 1.03 × 10 −7 eV / T. In the Purcell-Pound experiment described in Section 3.3, the maximum magnetic field strength was 0.63 T and the temperature was 300 K. Calculate the probability of a lithium nucleus being in each of its four spin states under these conditions. Then show that, if the field is suddenly reversed, the probabilities of the four states obey the Boltzmann distribution for T = −300 K.