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Addition of angular momentum

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Consider a deuterium atom (composed of a nucleus of spin I = 1 and an electron). The electronic angular momentum is J = L + S, where L is the orbital angular momentum of the electron and S is its spin. The total angular momentum of the atom is F = J + I, where I is the nuclear spin. The eigenvalues of J^2 and F^2 are J(J+I)h^2 and F(F+1)h^2 respectively.

(a) What are the possible values of the quantum numbers J and F for a deuterium atom in the 1s ground state?

(b) Same question for deuterium in the 2p excited state.

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The solution explains in detail how to find the quantum numbers of an atom when we add three angular momentum operators.

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