Physical Chemistry Third Edition

1026 24 Magnetic Resonance Spectroscopy

x

z

y

M(before 90° pulse)

M(after 90° pulse)

Precessing and

decaying path of

the component of M

in the x-y plane

Precessing

and decaying

M

y

x

z

M(after pulse)

M(equilibrium)

(a)(b)

Figure 24.7 (a) The Decaying and Precession of the Magnetization Vector. (b) The Decaying and Precession of the Component of the
Magnetization Vector in thex–yPlane.

1

0.75

0.5

0.25

0

2 0.25

y

0 1 2 3 4

x

1

0.75

0.5

0.25

0

2 0.25

2 0.5

2 0.75

0 1 2 3 4

y

x

(a) (b)

Figure 24.8 Two Decaying Oscillations Similar to FID signals.(a) A single frequency. (b) The sum of two frequencies.

The Spin–Echo Technique

This is the preferred method for measuringT 2 , the spin–spin relaxation time. Consider a

substance that has protons with several different chemical shifts. The procedure begins

with aπ/2 pulse (90◦pulse) that rotates the magnetization vector from thezaxis onto

theyaxis, as in simple Fourier transform NMR. Consider a substance with two protons,

A and B, that have different chemical shifts. Let the contribution toMfrom proton A