1) In class we explored the energy and entropy of a large group of N spin-1/2 protons ('H) when placed in a magnetic field. Let us extend this analysis to a group of N17O atoms. 17O is an isotope of oxygen with 8 protons +9 neutrons, which has spin 5/2. Thus upon application of a magnetic field, each nucleus can exist in one of six possible quantum states: mi=+5/2,+3/2,+1/2,1/2, 3/2, or 5/2, as illustrated below: These states are separated in energy by an amount hB0 (as they are for 1H ) and thus the total energy of a given nuclear spin (i) is Ei=(5/2mi)B0. If the nucleus is fully aligned with the magnetic field (m1=+5/2), its nuclear spin energy is zero. But it can be promoted to 5 higher energy levels, corresponding to increasing anti-alignment with the applied field, up to a maximum of Ei=5hB0 for mi=5/2. Our overall objective on this problem is to understand how entropy S and also the ensemble average of nuclear spin magnetization (M) depend on system energy U by considering a microcanonical (NVU) ensemble. a) Based on the description above, the total energy of a group of N17O nuclei is given by: U=i=1N(25mi)rhB0 where m, are the spin states of the individual nuclei (i=1,2,3,,N) Show that if all the nuclei have spin state m/=+1/2, the total energy of the system would be U=2NBe. Assuming the system remains isolated at this total energy, explain what would happen if one of the nuclei changed spin state from m=+1/2 to m=5/2