Consider a single spin 1 magnetic impurity in a magnetic field B = 104 Gauss (defining the z axis). The energy of such an impurity is given by E = ,u B 52 (with S2 = 1,0, 1), with u=10'20 erg/gauss. a) Compute the temperature at which the impurity has a 25% chance of being in its first excited state. b) Consider now an ensemble of N noninteracting such magnetic impurities at temperature T. Compute the partition function: Z c) Compute the mean energy E as a function of temperature d) Compute the heat capacity at high temperatures: CE = (BE/6T)B e) Compute the mean magnetization: M , verify that as T > 0, M = Nu