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a) We know that in terms of nuclear magnetons (and setting hbar to 1) we have \mu = g I. For the ground state the spin is 1/2 and the magnetic moment about -0.6 thus we have a g-factor of about -1.2, similarly for the excited state, the g-factor is -0.77*2/5 = 0.308
b) For a free electron we have spin 1/2 and magnetic moment= 1 bohr magneton, thus the g-factor is 2. Because there are two g-factors for the individual angular momenta, this formula is in units of bohr magnetons
c) We have a g-factor of -3.826 and a spin of 1/2, thus the magnetic moment in units of nuclear magnetons is about -1.9
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