From Eq.29 (see notes) one can see that the g-value can be calculated when the nuclear spin ‘I’ and the magnetic moment of the nucleus ‘u’ is known. From the tabulation, one can easily find that for the ground state these values are respectively -0.594 (nm) and 1/2. This results in a g-factor of -1,188, which is of the order of unity as is mentioned in the lecture notes.
For the excited state, the same raising is applied but different values are use. Now u = -0.77 and I = 5/2, resulting in a g-factor of -0.308.
* not sure what the ‘m’ in ‘mu_B’ is *
Given that it is a free electron, L = 0 and S = 1/2. Now Eq.29 can be modified to be applicable on electrons by interchanging u_N for u_B (Bohr magneton) and I for J = L + S, one the finds a value for g to be -2m.
Spin of the neutron is 1/2 and g = -3.826 and therefore the magnetic moment (in units of the nuclear magneton) has a value of -1.913.