1) The Zeeman splitting is given by -µB*gJ*B0*mJ, which yields:
-For mJ = -3/2: 0.138912 meV
-For mJ = -1/2: 0.046304 meV
So the energy of a transition photon would have to be 0.092608 meV
2) With hyperfine interaction turned on, the Zeeman levels are split into 2 levels (I=1/2) each with the splitting given by -gn*µN*B0*mI + A*mI*mJ, this gives:
-The mJ = -3/2 level is split into:
-mI = -1/2: 0.1946 µeV
-mI = 1/2: -0.1946 µeV
-The mJ = -1/2 level is split into:
-mI = -1/2: -0.0155 µeV
-mI = 1/2: 0.0155 µeV
-The mJ = 1/2 level is split into:
-mI = -1/2: -0.2257 µeV
-mI = 1/2 : 0.2257 µeV
The new transition energies will be those that correspond to energy differences between two levels with a difference in mJ of 1 and no difference in mI