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When an external magnetic field is applied, nuclear magnetic moments adopt only 2I + 1 available orientations instead of remaining randomly oriented. Orientations aligned with the field are lower energy, while those aligned against it are higher energy. This quantization of spin states is called Zeeman splitting, and the energy difference between states is directly proportional to the magnetic field strength.

A proton with nuclear spin I = ½ has two available orientations in a magnetic field. One orientation is aligned with the field at lower energy, and the other is aligned against the field at higher energy. This two-state system forms the basis of proton NMR spectroscopy.

The energy difference between spin states, ΔE, is directly proportional to the strength of the applied magnetic field. Stronger magnetic fields create larger energy separations between spin states. This relationship is fundamental to NMR, as it determines the frequency of radiofrequency pulses and pulse sequences needed to induce spin transitions.

Without an external magnetic field, nuclear magnetic moments are randomly oriented with no preferred direction. All orientations have equal energy, making the spin states degenerate. The external magnetic field breaks this symmetry by establishing a preferred axis, causing spin states to split into distinct energy levels.

Temperature influences which spin states are populated. As temperature decreases, lower-energy spin states become more populated than higher-energy spin states. This population difference is crucial for NMR sensitivity, as it creates a net magnetization that can be detected by the spectrometer.

A quadrupolar nucleus with nuclear spin I = 1 has three available orientations in a magnetic field. Using the formula 2I + 1, this yields 2(1) + 1 = 3 possible orientations. These three states have different energies based on their alignment relative to the applied magnetic field.

Zeeman splitting is the quantization phenomenon where an external magnetic field causes degenerate spin states to split into distinct energy levels. It occurs because the nuclear magnetic moment interacts with the applied field, creating an energy cost for orientations opposing the field. The magnitude of this splitting depends directly on the magnetic field strength.