Page 359 - Instant notes

Magnetic resonance spectroscopy 345

m I=I, (I−1),…, −I

The nuclear spin angular momentum quantum number can have a range of both integral
and half-integral values, as well as zero. Values for some common nuclei are shown in
Table 1.
Table 1. Nuclear spin quantum number and
abundance for some common isotopes

Isotope Natural abundance/% Spin I
1 H 99.98 ½
2 H 0.016 1
12 C 98.99 0
13 C 1.11 ½
14 N 99.64 1
16 O 99.96 0
17 O 0.037 5/2
19 F 100 ½

A nucleus with non-zero spin behaves like a magnet. In the presence of a magnetic field,
B (units tesla, T), the degeneracy of nuclei with the 2I+1 possible orientations of nuclear
spin angular momentum is removed. The states acquire different values of potential
energy:
E=−Bm Ig Iµ N

where g I is a numerical g-factor characteristic of the nucleus (and determined
−1
experimentally), and µ N=eћ/2m P is the nuclear magneton with value 5.05×10 −27 J T (m p
is the mass of the proton).
1
The two spin states (m I,=½ and m I=−½) of a hydrogen H nucleus in a magnetic field
(or any other nucleus with I=½) are separated by an energy (Fig. 1).

The Boltzmann distribution law dictates that slightly more nuclei will be in the lower of
the two energy states. Electromagnetic radiation of energy resonant with the energy
separation induces transitions between the two spin states and is strongly absorbed. The
resonance frequency, v=Bg Iµ N/h, is proportional to the strength of the magnetic field, and
is in the radiofrequency region of the spectrum.
In the practical application of Fourier Transf form NMR spectroscopy, the sample is
subjected simultaneously to a magnetic field and pulses of radiofrequency