Larmor precessional frequency

This velocity is called the Larmor precessional frequency. 

Now suppose that an additional small magnetic field is applied perpendicular to Ho in the plane formed by pi and Hq, call this field (see Fig. 4-4B). Field Hi will act upon pi to increase the angle 6. If field Hy is caused to rotate around Ho at the Larmor precessional frequency of Wq, the torque produced will steadily act to change the angle 6. On the other hand, if the frequency of rotation of Hi is not the same as the precessional frequency, the torque will vary depending upon the relative phases of the two motions, and no sustained effect will be produced. 

V (in Hz) by w = l-nv, comparison of Eqs. (4-43) and (4-44) shows that the Larmor precessional frequency is identical to the transition frequency that was calculated earlier. 

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

In Eq. (4-62) Wq is the Larmor precessional frequency, and Tc is the correlation time, a measure of the rate of molecular motion. The reciprocal of the correlation time is a frequency, and 1/Tc may receive additive contributions from several sources, in particular I/t, where t, is the rotational correlation time, t, is, approximately, the time taken for the molecule to rotate through one radian. Only a rigid molecule is characterized by a single correlation time, and the value of Tc for different atoms or groups in a complex molecule may provide interesting chemical information. 

The quantitative formulation of chemical exchange involves modification of the Bloch equations making use of Eq. (4-67). We will merely develop a qualitative view of the result." We adopt a coordinate system that is rotating about the applied field Hq in the same direction as the precessing magnetization vector. Let and Vb be the Larmor precessional frequencies of the nucleus in sites A and B. Eor simplicity we set ta = tb- As the frequency Vq of the rotating frame of reference we choose the average of Va and Vb, thus. 

Lagtime, 75 Laplace transform, 82 Larmor precessional frequency, 155, 165 Laser pulse absorption, 144 Lattice energy, 403 Law of mass action, 60, 125 Least-squares analysis linear, 41 nonlinear, 49 univariate, 44 unweighted, 44, 51 weighted, 46, 51, 247 Leaving group, 9, 340, 349, 357 Lennard-Jones potential, 393 Lewis acid-base adduct, 425 Lewis acid catalysis, 265 Lewis acidity, 426... 

After a 90° pulse, the bulk magnetization vector, M, is directed along the Y axis. The result of this simple experiment should be a single line, since there is only one vector that is rotating at exactly the same frequency as the Larmor precessional frequency. 

When excited by an applied alternating magnetic field the magnetization vector will precess around the anisotropy field as discussed more fully later (Section 9.3.4). Resonance occurs when the frequency of the applied field coincides with the natural precessional frequency, i.e. the Larmor frequency coL = yfi0HA, with the result that the permeability falls and losses increase, as shown for a family of NiZn ferrites in Fig. 9.29. The onset of such ferrimagnetic resonances restricts the use of MnZn ferrites to frequencies of less than about 2 MHz. At higher frequencies, up to about 200 MHz, compositions from the NiZn family are used. 

When an applied rf (vL) is equal to the precessional frequency of the equivalent protons (Larmor frequency in MHz), the state of nuclear magnetic resonance is attained, and the basic NMR relationship can be written ... 

Figure 50.1. The precession of the nuclear magnetic moment vectors p about the static magnetic field vector B. The angle of the precessional cone is given by 0. The precessional frequency is given by the Larmor frequency co.

The precessional motion can be maintained by a suitable radio frequency field superimposed on the steady field. For example, in Fig. 9.38(b), when a steady field Hz is applied along the z axis and a radiofrequency field //,., is applied in the x-y plane and rotates in the same sense and at the same frequency as the precession, resonance occurs. Gyromagnetic resonance as outlined above is in principle the same as ferrimagnetic resonance referred to earlier (Section 9.3.1), except that in the former case the material is magnetically saturated by a strong applied field. In practice the steady field, which determines the Larmor frequency, is made up of the externally applied field, the demagnetizing field and the anisotropy field, and is termed the effective field He. Figure 9.39 shows the He values at which resonance occurs in some of the important communications and radar frequency bands. 

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