Solutions will be posted December 4 evening - No late
homework accepted after solutions are posted
Calculate the energy difference between the normal and superconducting states
at T=0 using the critical magnetic field for Pb. Express your answer in eV per
valence electron. Compare this with the Fermi energy and
average kinetic energy per electron calculated in the free electron approximation.
State in your own words the argument for why a persistent
current can flow for very long times (times that could be longer than
the age of the universe!) in a ring of a type 1 superconductor.
Kittel problem 11-1. In this problem you are asked to
calculate the diamagnetic susceptibility for a hydrogen atom
using the known analytic form of the wavefunction.
You may use the formula: Integral of x4 exp(-x) from
0 to infinity = 4! = 24.
Calculate the paramagnetic spin susceptibility chi = dM/dB
evaluated at B=0 for a hydrogen atom in free space
at temperature 300K. The formulas valid for any temperature are
given in Kittel Ch 11, section on quantum theory of paramagnetism.
For this problem you only need the simplified formula valid for
small B. Compare with the magnitude of the
diamagnetic susceptibility from the previous problem.
Consider a solid with one electron spin per unit cell:
the maximum spin projection along any direction is m = 1/2 and the magnetization
(magnetic moment per unit volume) is M/V = (N/V) g m muB.
Calculate the maximum magnetization if the crystal
has the same atomic density as that of Fe.
Compare with the actual saturation magnetization of Fe.
(Relevant information is in Kittel.)