Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  183

compared to the nonmagnetic ¹²C and also a low sensitivity. Since carbon is a key component

of all organic compounds, it is widely used in NMR, but the ¹³C isotope has to be

included in the sample preparation process due to its low natural abundance. Other lesser

used isotopes include ¹⁵N (which has low sensitivity but is used since nitrogen is a key compo­

nent in proteins and nucleic acids), ¹⁹F (which has a high sensitivity, is rarely present in natural

organic compounds and thus, needs to be chemically bound into the sample in advance),

and ³¹P (which has a moderate sensitivity, and phosphorous is a key element of many biological

chemicals).

For a nuclear spin quantum number of I, the nuclear angular momentum L is given by

(5.14)

L

h

I I

=

+

(

)

2

1

π

where h is the Planck’s constant. The magnetic moment has discrete directionality such that

the angular momentum parallel to an arbitrary z-​axis Lz is given by

(5.15)

L

hm

z ⁼ 2π

where the magnetic quantum number, m, is allowed to take a total of (2I +​ 1) different values

of −I, −I +​ 1, I − 1, +​I. In the absence of an external magnetic field, all the different orientation

states have the same energy, for example, they are degenerate. The different spin states of the

nuclei have a different magnetic moment μ whose magnitude is given by

(5.16)

µ

γ

µ

γ

π

=

∴

=

L

hm

z

2

where

μz is the z component of μ

γ is a constant called the magnetogyric ratio (also known as the gyromagnetic ratio)

TABLE 5.2  Nuclear Magnetic Spin Properties of Common Half-​Integer Spin Nuclei

Isotopes Used in NMR (Bold) Compared Against Zero or Integer Spin

Atomic Nuclei (Not Bold)

Proton

Number (Z)

Neutron

Number (N)

Isotope

Nuclear Spin

Quantum

Number (I)

Natural

Abundance (%)

Magnetogyric

Ratio/​2π

(MHz T⁻¹)

Resonance

Frequency if ¹H is

400 MHz (MHz)

1 (odd)

0 (—​)

1H

1/​2 (half

integer)

99.998

42.6

400

1 (odd)

1 (odd)

2H (D)

1 (integer)

0.002

6.5

61.4

6 (even

6 (even)

12C

0 (zero spin)

98.89

0

—​

6 (even)

7 (odd)

13C

1/​2 (half

integer)

1.07

10.7

100.6

7 (odd)

7 (odd)

14N

1 (integer)

99.63

3.1

28.9

7 (odd)

8 (even)

15N

1/​2 (half

integer)

0.37

−4.4

40.5

8 (even)

8 (even)

16O

0 (zero spin)

99.757

0

—​

9 (odd)

10 (even)

19F

1/​2 (half

integer)

100

40.1

376.5

15 (odd)

16 (even)

31P

1/​2 (half

integer)

100

17.2

162.1