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The distribution of nuclei with different spins (denoted +: with external field, -:
against external field) is given by the Boltzmann formula:
ž
N
+
N
−
=
e
Δ
E
kT
≈
1
+
γ
h
2
π
⎛
⎝
⎞
⎠
B
kT
⎛
⎝
⎞
⎠
We can transfer spins from the lower energy level to the higher by
electromagnetic irradiation with energy corresponding to
Δ
E:
Δ
E = h
ν
Here
ν
is the frequency if the irradiation. Each nucleus therefore has a
characteristic resonance frequency:
ž
ν
=
γ
B
2
π
NMR instruments provide electromagnetic pulses at frequency
ν
to transfer
spins to the higher energy state. To excite protons (
1
H), the most common
nucleus in biomolecules, today’s magnets require frquencies in the range 300
– 800 MHz. NMR instruments detect the release of energy as excited nuclei
relax back to equilibrium.
If all protons in a molecule had exactly the same resonance frequency then
NMR would be of little use. The spectrum would for all compounds consist of
a single peak:
Fortunately, different protons have slightly different frequencies because the
external magnetic field B is modified by nuclear shielding. This modification is
caused by electrons within the molecule, and leads to the chemical shift (
δ
)
defined as:
ž
δ
=
B
reference
−
B
sample
B
reference
×
10
6
ppm =
ν
reference
−
ν
sample
ν
0
×
10
6
Figure 8.