Physical Chemistry Third Edition

24.5 Fourier Transform NMR Spectroscopy 1027

in all of the molecules be calledMAand that from proton B in all of the molecules

be calledMB. At the end of the first pulse,MAandMBwill both lie on the positive

yaxis. Since the protons A and B have different chemical shifts, they will precess at

slightly different rates. At a later time,MAandMBwill have precessed by different

angles in thexyplane, as depicted in Figure 24.9, where we assume thatMAprecesses

more rapidly thanMB. We say that the individual sets of spins with different chemical

shifts have begun todephase. After a length of time that is chosen by the experimenter,

aπpulse(180◦pulse) is imposed, which is twice as long as theπ/2 pulse. This pulse

rotates the magnetization vector by 180◦around thexaxis. The new directions ofMA

andMBare shown in the figure. The slower-precessing vector is now ahead of the

faster-precessing vector. The individual sets of spins continue to precess, but they now

draw closer to each other and reverse the dephasing. The magnetization vector returns

toward the value it had after theπ/2 pulse. This is the “spin echo.” Because of the

spin–spin relaxation, the component of the magnetization vector in thexyplane does

not completely return to its original value, with more of a difference for longer time

z

y

x

MA(after) MA(before)

MB(after)

MB(before)

Figure 24.9 Two Precessing Contributions to the Magnetization before and after the

180° Pulse.