2.Consider an AX spin system with one nucleus, and one nucleus I=1/2 nucleus, |I

Question

2.Consider an AX spin system with one nucleus, and one nucleus I=1/2 nucleus, |I,mI >, |1/2, -1/2> and one I=1 nucleus |I, mI> = |1,1>, |1,0>, |1,-1> and with a positive scalar coupling constant J.

a.What are the six possible spin states for the system using this notation: | mI (1), mI (2)>

b. Determine the energies of the six spin states (part a) using the Hamiltonian operator.

c. Draw an energy level diagram for the system and show the allowed transitions for each nucleus. ?mI= +/- 1(Assume that the spin

Explanation / Answer

Therer are only four possiblities related to the spin

        If m=0        +1/2 and -1/2

        If m=1         +1/2 and +1/2

        If m =0          -1/2 and +1/2

        If m =-1    -1/2 and -1/2

If ml =1

    spin will be (1/2 , 1/2)

If ml =2

         spin will be (1/2,1/2,1/2,1/2)

Hamaltoniam operator will be

       H =-gamma( Bo Sz)

             here gamma = gyrometric spin ratio =-ze/m

         H = -Ze / m (BoSz)

           Here Bo = external magnetic field

                  e = charge on proton

                  Z = number charges in nucleous

                    m = mass of nucleous

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