QUESTION 3 [TOTAL MARKS: 25] Consider a spin-flip system (e.g. a paramagnetic solid) composed of N = N,+N₂ = 6.0×102 single-electron spins localized at the nodes of a cubic crystal lattice. This system is in thermal equilibrium with a thermostat at absolute temperature T and immersed in a magnetic induction B. An electron spin in this system is equivalent to a tiny magnet bar and will tend to align its magnetic moment (spin vector) along the direction of the applied magnetic induction B thereby gaining (stabilizing) magnetic energy -μB. There are N, aligned spins in the crystal. If the electron magnetic moment aligns in the antiparallel direction to B the magnetic energy is +μB. There are N, anti-aligned spins in the crystal. Bohr magneton = 9.274x1024 Am2. The magnetic induction is B 2.0 T. The Boltzmann constant k = 1.38 x 10 JK¹. Q3(a) [4 marks] Represent this system on a diagram as a two-energy level system, discuss briefly the relative effects of increasing T or B and justify the use of Maxwell-Boltzmann statistics. Q3(b) [7 marks] Calculate the value of the characteristic temperature, of this system and, hence, the values of N, and N, and the total magnetic (stabilization) energy U of the system at T = 1.17 K. Q3(c) [4 marks] Give an expression for the partition function of the system q(T) in terms of O, and T and calculate its value at T=1.17 K.