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Isotopes and NMR

Only nuclei with an odd number of protons or neutrons exhibit a net nuclear spin, making certain isotopes suitable for NMR analysis.
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The statement of the theorem

Let NN be a nucleus with proton number ZZ and neutron number NeN_{e}. The nuclear spin angular momentum I\mathbf{I} is proportional to the total angular momentum of the constituent nucleons. For a nucleus to exhibit NMR activity, the net nuclear spin must be non-zero, i.e., I≠0\mathbf{I} \ne 0. This condition is met if the total number of nucleons A=Z+NeA = Z + N_{e} is odd, or if ZZ and NeN_{e} are both odd. Mathematically, the spin quantum number II must satisfy I=12∣Z−(Z mod 2)+Ne−(Ne mod 2)∣≥12I = \frac{1}{2} |Z - (Z \bmod 2) + N_{e} - (N_{e} \bmod 2)| \ge \frac{1}{2}. Isotopes with I=0I=0 (e.g., 12C^{12}\text{C}) are NMR inactive.