The g-factor can be calculated using the formula g = (µ hbar) / (µ_N I).
a) For the ground state of Cd^(111) we have I = 1/2 and µ = 0.595 nm. The g-factor is thus given by: g = 0.595 nm / µ_N * hbar * 2
For the 245 keV excited state, we have I = 5/2 and µ = -0.766 nm. We then obtain:
g = -0.766/µ_N * 2/5 * hbar
b)For the free electron, we have µ = µ_B and I = 1/2, the g-factor can be calculated to be:
g = 5.788 * 10^(-5) eV/T / µ_N * 2 * hbar
c) We can rearrange the formula to find:
µ = g µ_N I / hbar and then use I = 1/2 for the neutron to determine its magnetic moment.