Gyromagnetic moment

In this expression yn is the proton gyromagnetic moment and the dipolar second moment. This latter quantity is determined by the arrangement of the protons in the crystal structure and can be calculated if structural data are available for a given ternary hydride. It is also possible to derive the dipolar second moment from the NMR line shape. For a random walk diffusion process the mean jump time is related to the diffusion constant D via the expression (Cotts, 1972)... 

The proportionahty constant y is called the gyromagnetic ratio which is a function of the magnitude of the nuclear magnetic moment. Therefore each isotope having a net nuclear spia possesses a unique y. The y of some biologically relevant nuclei can be found ia Table 3. 

The values for the atomic saturation magnetization at the absolute zero, ferromagnetic metals iron, cobalt, and nickel are 2.22, 1.71, and 0.61 Bohr magnetons per atom, respectively.9 These numbers are the average numbers of unpaired electron spins in the metals (the approximation of the g factor to 2 found in gyromagnetic experiments shows that the orbital moment is nearly completely quenched, as in complex ions containing the transition elements). 

Sauer et al. [185] determined the gyromagnetic ratio g(9/2)/g(7/2) and the magnetic moment of the 6.2 keV level in Ta in two ways, (1) from the Zeeman split velocity spectrum of a metal source in a longitudinal field versus a Ta... 

Since /magnetic moment =y h 2ji), depends on the gyromagnetic ratio, /n. larger dipolar... 

Nuclide Spin I Electric quadmpole moment eQ (10-2 m2) Natural abundance (%) Relative sensitivity Gyromagnetic ratio y (103 radT- S-l)a NMR frequency (MHz) Bo = 2.3488 T)3... 

The angular momentum L has associated with it a magnetic moment /z. Both are vector quantities and they are proportional to each other. The proportionality factor y is a constant for each nuclide (i.e. each isotope of each element) and is called the gyromagnetic ratio, or sometimes the magnetogyric ratio. The detection sensitivity of a nuclide in the NMR experiment depends on y nuclides with a large value of y are said to be sensitive (i.e. easy to observe), while those with a small y are said to be insensitive. 

S is the sum of the spin quantum numbers, to which each electron contributes /2 and g is the gyromagnetic ratio, i. e. the ratio of the magnetic moment to the angular momentum. For a free electron, g = 2. 

This nuclear magnetic moment fl is represented by a vector that is colinear to I and has the same or opposite direction depending on the sign of 7, the gyromagnetic ratio (also called the gyromagnetic constant). 

By multiplying eq. (1.18) with the gyromagnetic ratio y one obtains the time dependence of the magnetic moment ft, remembering that fi = yp ... 

It is traditional to rewrite the definition of the nuclear magnetic moment in terms of magnetons and include a constant of proportionality called the gyromagnetic ratio or simply g factor ... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

The following table lists the gyromagnetic ratio, y, of some important nuclei that are probed in NMR spectroscopy.1-12 The gyromagnetic ratio is the proportionality constant that correlates the magnetic moment (p) and the angular momentum, p p = yp. 

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