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We can use the formula µ = gIµ_N, where µ is the magnetic moment, g is the g-factor and I is the nuclear spin. µ_N = (e \hbar) / (2m_p) is a nuclear magneton, a natural unit to express the magnetic moments. Its numerical value is 5.05 10^(-27) J/T
a) For the ground state, we find I=1/2 and µ=-0.59485 µ_N. We can calculate g = µ/(Iµ_N) = -1.1897. For the excited state, with I=5/2 and µ=-0.766 µ_N, we find g = -0.766*2.5 = -0.3064.
b) The electron has spin 1/2. This gives g = 1/I = 2, a well-known result.
c) µ = 1/2 x -3.826 µ_N = -1.913µ_N
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