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Magnetic resonance spectroscopy     349


                              intensity of each group of lines is also
                              shown.


        deshielding, and plus or minus the perturbation due to nucleus B, depending on whether
        the magnetic moment of B is aligned with or against the applied field. These two latter
        possibilities are equally likely. Therefore, a doublet resonance  of  equal  intensity  is
        observed at frequencies +½J A−B and  −½J A−B from the single resonance frequency that
        would be observed for A in the absence of coupling with B, where J A−B is the spin-spin
        coupling constant specific to A and B (Fig. 3). Since nucleus A has the same effect on
        nucleus B, the chemical shift for B is also split into a doublet with the same frequency
        separation J A−B.

















                              Fig. 3. The chemical shifts of two non-
                              equivalent protons are split into
                              doublets by spin-spin coupling.

        If there are two equivalent protons B present, the chemical shift of proton A splits into a
        triplet of lines of separation J A−B (Fig. 4). The intensity ratio of the triplet is 1:2:1 because
        there is one combination in which both B magnetic moments are aligned with the applied
        field, two combinations in which one B magnetic moment is aligned with the field and
        one aligned against the field, and one combination in which both B magnetic moments
        are aligned against the field. The concept is readily extended; N equivalent protons B
        split the chemical shift of  proton  A  into  N+1 lines with intensity ratio given by the
        coefficients of the Binomial expansion to power N+1 or, equivalently, to the (N+1)th line
        of Pascal’s triangle.
           In  general, spin-spin coupling in proton NMR spectra is only important between
        protons attached to adjacently bonded atoms. Couplings over larger numbers of bonds
        can be ignored.
           In the ethanol NMR spectrum (Fig. 2) the three protons of the CH 3 group split the
        single resonance peak of the CH 2 protons into a 1:3:3:1 quartet. The two
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