Physical Chemistry Third Edition

1024 24 Magnetic Resonance Spectroscopy

24.5 Fourier Transform NMR Spectroscopy

Most modern NMR spectrometers use the Fourier transform technique, similar to that

used in infrared spectroscopy. There is no need to scan the magnetic field, so spectra can

be taken quickly. The spectrum can be obtained repeatedly and the individual spectra

can be added, enhancing the signal and averaging out much of the noise. This is an

advantage with^13 C, which has a natural abundance of only 1% and therefore gives

only a weak NMR signal.

Fourier transform NMR spectroscopy can be described qualitatively in terms of the

classical picture ofLarmorprecession.^5 In a magnetic field, a magnetic dipole has a

torque acting on it, and this torque causes it to precess around the magnetic field in the

same way that the toy gyroscope depicted in Figure E.3 of Appendix E precesses about

the vertical direction. The direction of the dipole vector traces out a cone with the axis of

the cone in the direction of the field. If the magnetic dipole is produced by the orbiting

of a particle of chargeQand massmabout a center, its Larmor frequency (number of

revolutions about the cone per second) of the magnetic moment in a magnetic fieldB

is given by

νLarmor

1

2 π

Q

2 m

B (24.5-1)

The Larmor precession frequency of the magnetic moment of a proton is given by

νLarmor

1

2 π

gp

e

2 mp

B (24.5-2)

EXAMPLE24.17

Find the Larmor precession frequency of an unshielded proton in a magnetic field of 4.6973 T.

Solution

νLarmor

1

2 π

(5.5856)

1. 6022 × 10 −^19 C

2(1. 67265 × 10 −^27 kg)

(4.6973 T)

 2. 000 × 108 s−^1  200 .00 MHz

This precession frequency is equal to the frequency of the electromagnetic radiation that

induces the transitions involved in an NMR instrument. The term “magnetic resonance”

refers to the classical picture of the precession synchronizing itself with the radiation.

We discuss proton NMR, but our treatment also applies to other nuclei with spin

1/2, such as^13 C and^19 F. The two spin functionsαandβof a proton are like those of

electrons, and correspond to spin angular momenta that can lie in either of two cones of

directions, as depicted for electrons in Figure 17.12. The magnetic moment is parallel

to the angular momentum and must lie on one of the same two cones. The NMR sample

contains many molecules. In the presence of the external magnetic field the two spin

states will have slightly different energies, and slightly more of the protons will be

in the spin-up state than in the other, according to the Boltzmann distribution. From

(^5) R. S. Macomber,J. Chem. Educ., 62 , 212 (1985).