Practice question

When a proton couples to n equivalent neighbors of spin one-half, first-order theory predicts n+1 lines with intensity ratios given by binomial coefficients from Pascal's triangle. Two equivalent protons create four spin combinations: up-up, up-down, down-up, down-down, merging middle two to produce triplet with 1:2:1 intensities. Observing triplet therefore indicates adjacent methylene group, such as CH2 in ethanol or glutamate side chain. Coupling constant remains identical for both partners, allowing cross-validation of assignments in complex biomolecular spectra and metabolic pathway analysis.