Consider the hyperfine interaction Hamiltonian HHF = AÏ· J, where I and J couple to give the total angular momentum F = I + J. (a) Rubidium isotopes 85 Rb and 87Rb respectively have nuclear spins I = 5/2 and I = 3/2, with one valence electron. Sketch the hyperfine energy level diagram of the 5S1/2 and 5P3/2 states for each isotope. (b) The 651/2 level of 137Cs is split into two hyperfine sublevels with ex- perimentally observed splitting equal to 9.19 GHz. The nuclear spin of 137Cs is I = 7/2. Determine the hyperfine interval constant A.