We know formula mu = (g * mu_N * I) / hbar:

1.a): need g = (mu * hbar) / (mu_N * I)
– GS: mu = -0.5940 nm, I = 1/2+ ==> g = (-0.5940 [nm] * hbar) / (mu_N * 1/2)
– 1st excited state: mu = -0.766 nm, I = 5/2+ ==> g = (-0.766 [nm] * hbar) / (mu_N * 5/2)
(I do not know how to convert the units because mu is now given in nm in the database.)

1.b): need g = (mu * hbar) / (mu_N * I)
– free electron: I = 1/2, mu = mu_B ==> g = (mu_B * hbar) / (mu_N * 1/2)

1.c): need mu = (g * mu_N * I) / hbar
– free neutron: I = 1/2, g = -3.826 ==> mu = (-3.826 * mu_N * 1/2) / hbar