7.2: Atomic Nuclei: Nuclear Spin

All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.

Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to the nuclear spin value, and the same is true for neutrons.

The nuclei of carbon-12 and oxygen-16 contain even numbers of both protons and neutrons and have a zero net nuclear spin ( = 0). When the nucleus contains an odd number of protons (e.g., protium) or neutrons (e.g., carbon-13), the nuclear spin is a half-integer because of the unpaired nucleon. A nucleus containing odd numbers of neutrons and protons has a nonzero integer spin. All nuclei with nonzero spins are NMR-active.

Nuclei with spin values greater than ½ are called quadrupolar nuclei. More than two-thirds of naturally occurring NMR-active nuclei are quadrupolar (examples include nitrogen-14, oxygen-17, sulfur-33, boron-11, and chlorine-35). Quadrupolar nuclei have non-spherical charge distribution leading to asymmetric electric and magnetic fields that result in broad signals and complex NMR behavior. Consequently, spin-half nuclei, with spherical charge distribution and symmetric fields, are preferred for NMR studies.

All atomic particles possess intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of one-half.

Unlike electrons, protons and neutrons in nuclei may have higher spins, but the values are always half-integers.

All particles in a nucleus contribute to the overall nuclear spin, I.

In nuclei, protons pair with protons, and neutrons pair with neutrons. Paired particles contribute zero net spin to the nucleus. So, a nucleus with nonzero spin has at least one unpaired particle.

If the number of either protons or neutrons is odd, the nuclear spin is a half-integer because of the unpaired proton or neutron.

Likewise, if both the number of neutrons and protons is odd, the nuclear spin is a nonzero integer.  

Even though all nuclei with nonzero spins are NMR-active, spin-half nuclei — with spherical charge distribution and symmetric fields — are preferred for NMR studies.