Question

From MSU Graduate Qualifying Exam, Jan. 7, 1999:Consider a gas of noninteracting atoms in a magnetic field Bzeˆ in the z-direction. Each atom has total spin ½. Each atom has a permanent dipole moment, with magnitude m0, in the direction of the spin; for spin up m(vector) = m_0*e(hat)_z, and for spin down m(vector) = -m_0*e(hat)_z. The magnetic energy of the atom is -m_0*B for spin up, and m_0*B for spin down.

a) Determine the mean dipole moment of an atom as a function of the temperature T.(Recall that the probability for a system to be in a state with energy E is proportional to e^(-E/(KT))

b) Sketch a graph of the mean dipole moment versus T.

Answer 1