Instant Notes: Analytical Chemistry

All nuclei are assigned a spin quantum number, I, on the basis of the number of

protons and neutrons in the nucleus, the values being zero, half-integral or

integral. The number of permitted orientations in space and hence quantized

energy levels, or spin states, that can be adopted by a nucleus subjected to an

externally applied magnetic field is given by (2I + 1). Thus, for I=^1 ⁄ 2 , two orien-

tations, or energy levels, are possible. The following should be noted.

● A spinning nucleus, being charged, generates a magnetic moment vector, or

dipole, along its axis of rotation. This is analogous to the magnetic field asso-

ciated with a current flowing in a loop of wire (Fig. 3a).

● Nuclei with even numbers of both protons and neutrons, e.g.^12 C,^16 O and

(^32) S, have a spin quantum number of zero, no spin angular momentum or
magnetic moment, and can not give an NMR spectrum.
● Nuclei with a spin quantum number of^1 ⁄ 2 , and therefore two spin states,
include the proton, carbon-13, phosphorus-31 and fluorine-19 (Table 1).
● An electron also has spin, but being of opposite charge to a nucleus, it
produces a magnetic moment vectorin the opposite direction (Fig. 3a).
Electrons also circulate under the influence of an applied field, generating
additional fields that modify those experienced by the nuclei (Fig. 3b).
Chemical shift The applied magnetic field experienced by a nucleus is affected by the fields
generated by surrounding electrons, which may augment or oppose the external
field. The effective field, Beff, at the nucleus may be defined as
Beff=Bo(1 - s) (3)
where sis a shielding constantwhich may be positive or negative. The
resonance frequency, defined by equation (2), is therefore given by
n= (g/ 2 p) ·Bo(1 - s)orn= (g/ 2 p) ·Beff (4)
Consequently, nuclei in different chemical environments will have slightly
different resonance frequencies due to shieldingor deshielding by nearby
Nuclear and
electron spin
E12 – Nuclear magnetic resonance spectrometry: principles and instrumentation 251

Electron

+

Angular momentum

vectors

I

Proton

Magnetic moment

vectors

m Nucleus

DB 0

Circulating

electrons

Secondary field

(a) (b)

Fig. 3. (a) Spin angular momentum and magnetic moment vectors for a nucleus and an electron; (b) magnetic field
induced by circulating electrons.