Other Instrumental Methods in Environmental Analysis - Fundamentals of Environmental Sampling and Analysis - page 324

nuclei behave like tiny bar magnets. Some nuclei will align with the magnetic field (at a
lower energy level), whereas others will align against the field (at a higher energy
level). Since the nucleus energy is quantized, there will be no other spin states. The
energy difference between the two nuclear spin states is as follows:

gh
2p B 0

E ¼ ð12 : 1Þ

where h is the Planck's constant, B 0 is the strength of the magnetic field in the unit of
tesla (T), and g is the gyromagnetic ratio in the unit of rad/T/s. One tesla (T) is actually
a relatively strong field—the earth's magnetic field is of the order of 0.0001 T.
When an electromagnetic radiation is introduced, the nucleus is resonated if the
applied radiation energy (E ¼ hn) is equal to the energy difference (

E) noted in

Eq. 12.1. This frequency can be calculated by

g
2p B 0

n ¼ ð12 : 2Þ

At the resonance frequency, nuclei in the lower energy (þ½) flip to the higher energy
state (½). Since the value of gyromagnetic ratio (g) depends on a particular kind of
nucleus, different energies are required to bring different kinds of nuclei into
resonance. Hence, an NMR signal (rf absorption) can be obtained as a function of the
changing frequency. Such a relationship is the basis of an NMR spectrum.
Note that only certain atomic nuclei have the NMR signals. Nuclei with an even
mass number and an even charge number ( 12 C) have spin quantum numbers of zero.
Nuclei with an even mass number and an odd charge number (e.g., 2 H) have integer
spin quantum number of one. Neither 12 C nor 2 H produces NMR signals. Only
nuclei with odd mass numbers and half-integer spin quantum numbers (I ¼ ½),
such as 1 H, 13 C, 15 N, 19 F, and 31 P can be used to obtain NMR spectra. Among
these, 1 H and 13 C are the most common, hence the name 1 H-NMR (proton NMR)
and 13 C-NMR (carbon thirteen NMR).
From Table 12.2, it is clear that the most abundant isotope of carbon ( 12 C),
unfortunately, cannot be used to obtain an NMR spectrum. The NMR responsive

Table 12.2 Properties of selected nuclei that are important in NMR spectroscopy a

Natural Gyromagnetic NMR frequency Relative

(MHz) b sensitivity c

Nucleus Spin (I) abundance (%) ratio (rad/T/s)

1 H

½ 99.99 2:675210 8 100 1

2 H

1 0.01 4:106610 7 15.35 9:6510 3

12 C

0 98.9 - - -

13 C

½ 1.1 6:728310 7 25.15 1:5910 2

14 N

1 99.6 1:933810 7 7.23 1:0110 3

15 N

½ 0.4 2:712610 8 10.14 1:0410 3

19 F

518210 8 3210 1

½ 100 2 : 94.09 8 :

31 P

1:084010 8 6:6510 2 ½ 100 40.48

a Values adapted from Friebolin (2005).
b NMR resonance frequency is calculated at B 0 ¼ 2:3488 T.
c Selectivity is expressed relative to 1 H at a constant field for an equal number of nuclei.