i) Ce (Z=58) and Nd (Z=60) are crucial for industrial uses because of their magnetic characteristics. Discuss why they make up some of the most powerful magnets attainable using the formula connecting the magnetic moment and angular momentum along with the atomic structure of these materials.

ii) Draw the level-energy diagram for an atom with linked angular momentum j=5/2 as a function of magnetic field B0 using the center region of the Rabi experiment as the starting point. Describe briefly what occurs when the Lamour frequency becomes equivalent to the frequency of the exterior duration-rotating magnetic field B(t) in the x-y plane and give an explanation of how the needed frequency is functionally dependent on the energies of the relevant states.