Suppose that an NMR sample containing 1013 protons is placed in a magnetic field of 9.4 T. Using the Boltzmann distribution, calculate the equilibrium populations of the α and β levels, assuming that the temperature is 298 K.
When the sample is first placed in the magnetic field, half the protons will be in the a level and half will be in the B level. Calculate the total energy change of the spins when they go from this initial state to equilibrium. Compare your answer with the typical thermal energy possessed by N molecules, which is of the order of NkBT.