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edited by: RON DELORENZO
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and analogief An Analogy of the NMR Effect Albert W. M. Lee Hong Kong Baptist College 224 Waterloo Road Kawlwn. Hong Kong
I found that some of my first year organic chemistry students, especially those without a good physics background, have difficulties grasping the meaning of the underlying principles involved in NMR. The alignment and the opposition of a compass needle to the earth's magnetic field has been widely used as a simple illustration of energy separation of the two spin states under the influence of an external magnetic field and the spin flipping concept. The analogy des6rihed herein uses the differenrr in energy between standing upright and on one's head in the earth's eravitational field. The principle of the NMR efflct is based on the fact that a nucleus with soin anenlar momentum ouantum number ( I ) not equal to zero will generate a magnetichipole moment (PI). When such a nucleus is introduced into a uniform magnetic field of strengthB0, the magnetic moment will precess about the axis of the external field. The precessing magnetic moment vector cannot point in any arbitrary direction. For protons (I = %),there are onlv two oossible orientations. as eoverned bv themagnetic spin &t&n number (MI), which c& only have the value f'12 for a proton (fig., a). When the quantum of energy satisfying the resonance condition is absorbed, the nucleus will "flip" from its low spin state (MI = +'/.) to the high spin state (MI = -'/2). The magnetic dipole moment itself does not produce the resonance phenomena. I t needs an external magnetic field to separate the energy levels of the two spin states. Similarly, different orientations of a human body with res p e d to the earth's gravitational field (G) may correspond to different energy states. In the absence of the gravitational field (imagine you are in space, G = O), there is no difference in gravitational potential energy between standing upright and standing upside down. Actually, one would not have the feeling of u p or down in space unless there were a reference object. Under this zero-field situation, the up and the down states. which are eaual in enerw. are said to be deeenerate. As the field strength increases, the two degenerate s g t e s split and become unequal in enerw. The students should easilv accept the fact that standing upside down, which corresponds t o the 4 2 spin state of a nucleus, is the higher energy state. The direct proportion of the energy difference between the up and down states to the external field strength can be further illustrated by comparing the situation on the earth's
This feature presents a collection of desniptive applications and analogies designed to help students understandsome of the difficun concepts hequently encountered in chemistry. Contributions that will produce a greater appreciation arm knowledgeof political, religious, economic, historical, and scientific aspects of life are encouraged.
Middle Georgia Collage Cochran. Georgia 31014
surface to that on the moon's. Standing upside down on the moon's surface, where gravitational field strength is roughly one-sixth that of the earth's, requires less energy. This clearly points out that the energy difference is diminished as the field strength is reduced (fig., b). Only those nuclei with nonzero spin will show the NMR effect. A nuclei with zero spin (I= 0, e.g., 12C, 160) will retain its dezeneracv no matter how strone the external maenetic field might he. Similarly, the presence-of the gravitational tield is not the only factor which determines whether there will be energy separ&ion between different orientations of an object. If a spherically symmetric object has its center of gravity right a t its geometric center, there would be no difference in potential energy with respect to orientation for any field strength. The ratio of proton population in the two spin states is governed by the magnitude of the energy separation. In proton NMR, the energy separation betwden the +'I2 and -'I2 spin is very small (about 4 X 10W6 joule in a 1.4-tesla field). At room;emperaturc, hoth spin states are nearly equally p;,pulated according to the Rultrrnann's law of distrihution. In contrast, the difference in potential energy between the up and the down state of a human hodv on earth is relativelv- laree as compared to the nuclear spin case, because the center of gravity of the human bods is relatively far from its geometric Eentei and the earth's gravitational-field is com~aratively large. Ignoring the anatomy of legs and arms, this large dif'Terence in potential energy is respbnsihle for the her that the lower energystaw (standing up) is heavily populawd, i.e., no ~. one on earth walks on his or her hands. T o eoualize the DOD.. ulation, one must go to a tiny planet with a very small gravitational field. One would not be surmised to find that almost half of the population there enjoyeh walking on their hands since the enerw difference between the two orientations is Although every. nalogy has its own limitations, a relevant one such as this should appeal to students' common sense in this aee of soace travel. I have used this analow in mv" oreanic chemistry class, which consists primarily of biology majors, and I have found that the response was quite positive.
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Earth C
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Mwn
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Space G=O
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An analogy between body oriemations in the gravitational field (@and nuclear spin wiemations wilh respen to an external magnetic field (Bo).
Volume 62 Number 4
April 1985
319
