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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 413
zz(0, 0)
r
θ
δz
Figure 12.1
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
0.0
0.5
1.0
1.5
2.0
z/r
In
te
ns
ity
Figure 12.2
D12B.4 �is is discussed in detail in Section 12B.3(d) on page 503. In summary, two
nuclei are chemically equivalent if they are related by a symmetry operation of
the molecule. Such nuclei will have the same resonance frequency, that is, the
same chemical shi�. Examples are the protons in benzene, and H-2 and H-6 in
4-nitrophenol. In benzene the protons are related by a C6 operation (as well as
others) and in 4-nitrophenol the protons are related by re�ection in a mirror
plane perpendicular to the plane of the ring and passing through C-1 and C-4.
Two chemically equivalent nuclei A and A′ are magnetically equivalent if the
coupling between A and any other magnetic nucleus in the molecule, say Z,
is the same as the coupling between A′ and Z. If Z itself is to be magnetically
equivalent to Z′, then the couplings A–Z, A–Z′, A′–Z, and A′–Z′ must all be
equal: that is, the couplings between anymember of a group of equivalent spins
with any member of another group of equivalent spins must be the same in
order for the groups each to be magnetically equivalent.
For example, in PF5, which has a trigonal bi-pyramidal structure, the three
equatorial �uorines are magnetically equivalent, as are the two axial �uorines.