Consider a system consisting of N noninteracting atoms in asubstance at temperature T and volume V placed in an externalmagnetic field B pointing in the z direction. The magnetic energyof an atom can be taken as
e=-µiB
where µ is the magnetic moment of the atom. In this problem, wewill not consider the detailed contributions to the atomic magneticmoment from both the orbital and electron spin angular momentum;rather we will take the atomic magnetic moment to simply be givenby
µ=-gµBJ/?? in terms of the atomic g-factor, Bohr magneton, and thetotal angular momentum of the atom.
(a) Write the energy per atom noting that the magnetic field is inthe z direction. (b) Given that the magnitude and z component ofthe total angular momentum are
quantized, write the energy per atom in terms of the magneticquantum number mj , indicatingtherangeoftheallowedmjvaluesintermsofj,thequantumnumber associated with the magnitude ofthe total angular momentum. (For electron spin, j = 1/2 and mj = ±1/2.)
(c) How many values of mj are there?
Consider a system consisting of N noninteracting atoms in asubstance at temperature T and volume V placed in an externalmagnetic field B pointing in the z direction. The magnetic energyof an atom can be taken as
e=-µiB
where µ is the magnetic moment of the atom. In this problem, wewill not consider the detailed contributions to the atomic magneticmoment from both the orbital and electron spin angular momentum;rather we will take the atomic magnetic moment to simply be givenby
µ=-gµBJ/?? in terms of the atomic g-factor, Bohr magneton, and thetotal angular momentum of the atom.
(a) Write the energy per atom noting that the magnetic field is inthe z direction. (b) Given that the magnitude and z component ofthe total angular momentum are
quantized, write the energy per atom in terms of the magneticquantum number mj , indicatingtherangeoftheallowedmjvaluesintermsofj,thequantumnumber associated with the magnitude ofthe total angular momentum. (For electron spin, j = 1/2 and mj = ±1/2.)
(c) How many values of mj are there?
