Recall our problem involves a group of N non-interacting spin- 5/2 nuclei in a lattice, each of which can exist in one of 6 energy levels given by spin quantum number: mi=+5/2,+3/2,+1/2,1/2, 3/2, or 5/2, as illustrated below: a) Show that any individual nucleus has molecular partition function q given by: q=k=05ekB0 b) Derive an expression for the normalized probability Pk of a nucleus being found in energy state Ek as a function of scaled temperature T=kbT/hB0. Make a ListPlot or BarChart of Pk vs. k at T=0.001,1,10, and 1000. Explain the behavior you see. c) From the result of part a, show that the scaled energy per nucleus u=U/(NhB0), and the scaled entropy per molecule s=S/Nkb, are given by: u=k=05kPks=ln(q)Tu