1a: I know that g = (mu h_bar) / mu_N I
This gives that g_gs = ((-0,5940) h_bar)/(mu_N * 1/2) and g_ex = ((-0,766) h_bar)/(mu_N * 5/2)

1b: mu = g*mu_B*S/h_bar for electrons and mu = mu_B so g = h_bar/S = 2 h_bar
1c: mu = (g * mu_N * I)/h_bar = (-3,826 mu_N 1/2)/h_bar