Splitting patterns observed in proton nuclear magnetic resonance (NMR) spectroscopy arise from the phenomenon of spin-spin coupling between neighboring hydrogen atoms within a molecule.

In proton NMR spectroscopy, the splitting or multiplicity of a signal results from interactions between the magnetic fields of adjacent hydrogen atoms. This interaction is termed spin-spin coupling. It is crucial to understand that this effect occurs exclusively between hydrogen atoms that are bonded to adjacent carbon atoms, commonly referred to as ‘coupled’ hydrogens.

The number of peaks in a splitting pattern can be predicted using the ‘n+1 rule’. According to this rule, if a hydrogen atom has $n$ neighboring hydrogen atoms, it will exhibit $n+1$ peaks in its NMR signal. For instance, if a hydrogen atom is adjacent to two other hydrogen atoms, it will produce three distinct peaks.

The intensities of these peaks follow the distribution seen in Pascal’s triangle, where the outer peaks are smaller and the inner peaks are larger. This intensity pattern arises from the differing probabilities of the neighboring hydrogen atoms aligning with or against the applied magnetic field.

The distance between the peaks in a splitting pattern, known as the coupling constant ($J$), quantifies the strength of the spin-spin coupling. This value remains consistent across all peaks in a given splitting pattern and is independent of the strength of the external magnetic field.

In summary, the splitting patterns in proton NMR provide critical insights into the molecular structure. By analyzing these patterns, chemists can infer the number and arrangement of hydrogen atoms in a molecule, which assists in the identification of unknown compounds. For further exploration of the principles and applications of NMR spectroscopy, please refer to our comprehensive discussion on the topic.