Physical Chemistry , 1st ed.

mge



BSg

e



B



1

2

 

3

2

^

2.002 

6.626

2

1



0 ^34 Js)

 

3

4



2.002(9.274  10 ^24 J/T) ^3

4



where we have used the fact that SS^2 ^12 (^12 

1) 

2



^34 

. The mag-
netic moment of an electron is thus ()1.608  10 ^23 J/T. (It is negative, but
in many cases the absolute value of the magnetic moment is used, so the neg-
ative sign is ignored.) The two reasons for the difference in the magnetic mo-
ments are the different gfactors and the different masses of the particles.

Because certain nuclei have a magnetic dipole, they experience a potential

energy when they are subjected to a magnetic field. As with electrons, there are

2 I 1 different possible orientations of the nuclear spin when subjected to a

magnetic field, and each orientation has its own change in total energy Emag.

In the presence of a magnetic field, then, these different potential energies split

into individual levels, and electromagnetic radiation of just the right energy

can cause a nucleus to go from one nuclear-spin orientation to another. The

change in the energy is similar to that for ESR:

EmaggNNBMI (16.20)

where gNis the gfactor for the particular nucleus,Nis the nuclear magneton,

Bis the magnetic field strength, and MIis the quantum number for the zcom-

ponent of the nuclear angular momentum, which can have 2I 1 possible val-

ues. We are using MIinstead ofMI,zbecause we are now considering only a

single nucleus, not a combination of different atomic nuclei. Note how equa-

tion 16.20 is similar to equation 16.14. Table 16.1 lists the nuclear properties

gNand Ifor various nuclei. Figure 16.13 shows the splitting of the MInuclear

levels for nuclei having I3 and exposed to a magnetic field.

Because different nuclei have different nuclear spins Iand different possible

zcomponents of the nuclear spins MI, you might think that a specific formula

for the expected energies of transitions would be difficult to determine, but

that is not the case. There is a selection rule regarding changes in the MIquan-

tum number:

MI

 1 (16.21)

and for absorption spectra it becomes simply MI1. (We did not formally

consider a selection rule for ESR transitions.) Using this fact, we can come up

with equations similar to equations 16.15 and 16.16 to relate the resonant fre-

quency or wavelength of light that will be absorbed by a nucleus in a magnetic

field. They are

 ̃resgN

h



c

NB (in cm^1 ) (16.22)

res

gN

h

NB (in s^1 ) (16.23)

where all of the variables have previously been defined. The first equation

yields a wavelength in units of wavenumbers, and the second equation gives

(9.274  10 ^24 J/T)



(6.626  10 ^34 Js)/2

16.5 Nuclear Magnetic Resonance 573

Table 16.1 Two properties of

various nuclei

Nucleus Spin,I Nuclear gfactor,gN

(^1) H  (^12)  5.586
(^3) He  (^12)  4.2548
(^6) Li 1 0.8220
(^11) B  (^32)  1.7923
(^13) C  (^12)  1.405
(^19) F  (^12)  5.2567
(^31) P  (^12)  2.2634
(^209) Bi  (^92)  0.8975
B  0 B  0
I  3
Energy
MI   3
MI   2
MI   1
MI  0
MI   1
MI   2
MI   3
Figure 16.13 In the presence of magnetic
fields, nuclear spin states split into nondegenerate
energy levels. NMR spectroscopy probes the tran-
sitions between these nuclear energy states.