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430 12MAGNETIC RESONANCE
328.865, 330.975, 331.735, 331.755, 333.845, 333.865, 334.625 and 336.735 mT
All 8 lines have equal intensity . However, the third and fourth peak, and the
��h and sixth peak, are closely spaced and so, if the instrument does not have
high enough resolution, may overlap with one another to give a peak of double
height.
E12D.4(b) (i) �e expectation is that the CH2 protons will have a larger hyper�ne con-
stant than the CH3 protons. �erefore the main splitting will be into
a triplet (1:2:1), and each of the lines of the triplet may be further split
by a smaller amount into a quartet (1:3:3:1). If all the lines are resolved
the spectrum will be a triplet of quartets, a total of 12 lines with relative
intensities 1:3:3:1; 2:6:6:2; 1:3:3:1.
(ii) �e splittings due to couplings to equivalent spin 1 nuclei are illustrated in
Fig. 12D.5 on page 521. Coupling to the CD2 deuterons will give �ve lines
with intensities (1:2:3:2:1).�e smaller coupling to the CD3 deuterons will
split each of these lines into seven, with intensities (1:3:6:7:6:3:1), giving
35 lines in total.
E12D.5(b) �e resonance frequency is related to the g-value by [12D.2–519], hν = gµBB0.
Rearranging this gives B0 = hν/µB.
(i) For a spectrometer operating at 9.501 GHz,
B0 =
hν
gµB
= (6.6261 × 10−34 J s) × (9.501 × 109 Hz)
2.0024 × (9.2740 × 10−24 J T−1)
= 339.0 mT
(ii) For a spectrometer operating at 34.77 GHz,
B0 =
hν
gµB
= (6.6261 × 10−34 J s) × (34.77 × 109 Hz)
2.0024 × (9.2740 × 10−24 J T−1)
= 1.241 T
E12D.6(b) If a radical contains N equivalent nuclei with spin quantum number I, then
there are 2NI+1 hyper�ne lines.�e radical contains twomagnetic nuclei,N =
2, and there are a total of �ve hyper�ne lines.�erefore 2NI+1 = 2×2×I+1 = 5
hence I = 1 . �e splitting pattern arising from coupling to equivalent nuclei
with I = 1 is shown in Fig. 12D.5: coupling to two such nuclei gives �ve lines in
the intensity ratio 1:2:3:2:1.
Solutions to problems
P12D.2 �e EPR resonance condition is given by [12D.2–519], hν = gµBB0, where ν is
the spectrometer operating frequency, g is the g-value of the radical, µB is the
Bohr magneton and B0 is the magnetic �eld. �e expression is rearranged to
make g the subject.
When the applied magnetic �eld is parallel to the OO direction,
g = hν
µBB0
= (6.6261 × 10−34 J s) × (9.302 × 109 Hz)
(9.2740 × 10−24 J T−1) × (333.64 × 10−3 T)
= 1.992