Magnetic properties of nuclei

FIGURE 3.1 Spinning charge on proton generates magnetic dipole. 

Relevant properties, including the spin number, 7, of several nuclei are given in Chapter 6, Appendix A. The spin number 7 can be determined from the atomic mass and the atomic number as shown in Table 3.1. 

TABLE 3.1 Type of nuclear spin number, /, with various combinations of atomic mass and atomic number. 

Nuclei with a spin number 7 of one or higher have a nonspherical charge distribution. This asymmetry is described by an electrical quadrupole moment, which, as we shall see later, affects the relaxation time and, consequently, the linewidth of the signal and coupling with neighboring nuclei. In quantum mechanical terms, the spin number 7 determines the number of orientations a nucleus may assume in an external uniform magnetic field in accordance with the formula 27+1. We are concerned with the proton whose spin number 7 is 1/2. 

The radiofrequency energy p, can be introduced either by continuous-wave (CW) scanning of the frequency range or by pulsing the entire range of frequencies with a single burst of radiofrequency energy. The two methods result in two distinct classes of NMR spectrometers. 

The tendency toward +z precession in the presence of Bq is defined by Boltzmann s law. 

The precessional motion of the magnetic moment around Bq occurs with angular frequency wq, called the Larmorfrequency, whose units are radians per second (rad s ). As Bq increases, so does the angular frequency that is, coq cx Bq, as is demonstrated in Appendix 1. The constant of proportionality between o o and Bq is the gyromagnetic ratio 7, so that wq = Bq. The natural precession frequency can be expressed as linear frequency in Planck s relationship AE = Hvq or angular frequency in Planck s relationship AE = h(x)Q (coq = 2 rrvo). In this way, the energy difference between the spin states is related to the Larmor frequency by the formula 

The foregoing equations indicate that the natural precession frequency of a spinning nucleus (coq = 7B0) depends only on the nuclear properties contained in the gyromagnetic 

Because gyromagnetic ratios vary among elements and even among isotopes of a single element, resonance frequencies also vary (wq = 7R0)- There is essentially no overlap in the resonance frequencies of different isotopes. At the field strength (7.05 T) at which protons resonate at 300 MHz, nuclei resonate at 75.45 MHz, nuclei at 30.42 MHz, and so on. 

When spins have values greater than there are more than two available spin states. For I = 1 nuclei such as H and N, the magnetic moments may precess about three directions relative to Bq parallel (/, = -fl), perpendicular (0), and opposite (-1). In general, there are (21 + 1) spin states—for example, six for I = 5/2 ( O has this spin). The values of L extend from +/ to — / in increments of 1 ( + /,+/ — 1, +/ — 2. —/). Hence, the energy-state picture is more complex for quadrupolar than for spherical nuclei. 

The spin of a nucleus may be described in terms of two quantum numbers the spin quantum number, or spin /, and the spin magnetic quantum number, or projection m/. The two numbers are related as shown in the equation 

for a nucleus, the number / can take only two values, 1 or the number m/ can take only values 0, 5, and 1. From / and m/, two quantities, / and 7, are defined  

The nuclear magnetc moment p is expressed in terms of the nuclear g factor, gi, and the nuclear magneton, p , by using equations 

The proportionality constant is expressed as y and is called the magnetogyric ratio of the nucleus, 

There is, however, a slight difference in the values of the quantum numbers between the electron and the nuclei. The electron spin can only have two possible projections 5 in a given direction. The spin quantum number I for a nucleus can have a value different fiom (i.e., 1). 

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Nuclear magnetic resonance spectroscopy is a technique that, based on the magnetic properties of nuclei, reveals information on the position of specific atoms within molecules. Other spectroscopic methods are based on the detection of fluorescence and phosphorescence (forms of light emission due to the selective excitation of atoms by previously absorbed electromagnetic radiation, rather than to the temperature of the emitter) to unveil information about the nature and the relative amount specific atoms in matter. 

The NMR phenomenon is based on the magnetic properties of nuclei and their interactions with applied magnetic fields either from static fields or alfemaling RF fields. Quanfum mechanically subatomic particles (protons and neutrons) have spin. In some nuclei these spins are paired and cancel each other out so that the nucleus of the atom has no overall spin that is, when the number of protons and neutrons is equal. However, in many cases the sum of the number of protons and neutrons is an odd number, giving rise to... 

Nuclear relaxation rates, iron-sulfur proteins, 47 267-268 Nuclear resonance boron hydrides and, 1 131-138 fluorescence, 6 438-445 Nuclear spin levels, 13 140-145 Magnetic properties of nuclei, 13 141-145 Nuclear testing... 

H NMR spectrometry is the foundation upon which we will build an understanding of the magnetic resonance of other nuclei, especially 13C, which leads to the important advanced correlation experiments. We began by describing the magnetic properties of nuclei, noting the special importance of spin 1/2 nuclei. For practical... 

NMR spectroscopy exploits the magnetic properties of nuclei to give important qualitative and quantitative information on biological samples. There are various different forms of this important technique, but in each case NMR spectroscopy relies on fundamental NMR theory discussed earlier. 

Edward Mills Purcell (1912-1997) and Felix Bloch did the work on the magnetic properties of nuclei that made the development of NMR spectroscopy possible. They shared the 1952 Nobel Prize in physics. Purcell was bom in Illinois. 

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