Larmor angular frequency

From equation (5.61), the Larmor angular frequency or velocity o l is equal to the velocity of the end of the vector L divided by the radius of the circular path shown in Figure 5.5... 

Protons bound to a magnetic particle with adsorption sites characterized by different Larmor angular frequency shifts (8c0i) will progressively become out of phase, and the signal S(t) will decay according to... 

Electron spin quantum component Electron spin quantum number Hyperhne coupling constant Larmor angular frequency Larmor frequency Magnetogyric ratio Nuclear magneton Nuclear spin quantum component Nuclear spin quantum number Orbital quantum number Orbital quantum number component Principal quantum number Quadrupole moment Relaxation time longitudinal transverse Shielding constant... 

Strength and the sample concentration, po is the permeability of free space, Q is the quality factor of the coil, coo is the Larmor angular frequency, K is the volume of the coil, F is the noise figure of the preamplifier, k is Boltzmann s constant, is the probe (as opposed to sample) temperature, and A/is the bandwidth (in Hz) of the receiver. It can be seen that the concentration sensitivity 5c (SIN per pM concentration of analyte) is poor for microcoils. This is due to the fact that microcoil probes have very small observation volumes and therefore contain a very small amount of analyte. However, if the sample can be concentrated into a small volume, then the microcoil can more easily detect the signal. This high mass sensitivity 5m (SIN per pmol of analyte) is characteristic of microcoil NMR probes. In essence, the use of microcoil probes enhances the mass sensitivity 5m at the expense of the concentration sensitivity 5c. To better understand the relationship between sensitivity and coil diameter, a detailed analysis was reported by Peck et Their results showed that mass sensitivity increases monotonically with decreasing coil diameter within the 1mm to 50 pm range they studied. However, the concentration sensitivity decreases, and therefore there is a trade-off between Sc and 5m that depends on coil diameter. 

When an external magnetic field B is applied in the z direction, the oscillating electron experiences a Lorentz force e(yxB) which causes the plane of oscillation to process about the field direction with the Larmor angular frequency... 

From equation (3.83) we see that the external magnetic field removes the degeneracy of the fine-structure states y LSJMj >. In weak magnetic fields a set of equally spaced magnetic sub-levels is produced separated by energies of where = gj UgB/h is the Larmor angular frequency. 

This solution corresponds to a precession of the. magnetic dipole about the direction of the magnetic field at the Larmor angular frequency = yB with y inclined at some constant but arbitrary angle 6, as shown in Fig.16.3. 

Hence prove that p precesses at the Larmor angular frequency u)j =yB about the direction of the applied field. 

In this experiment the magnetic dipole moment of an atom which has just completed the optical pumping cycle at time tQ finds itself pointing along the Ox axis. Immediately afterwards it starts to precess about the magnetic field B at the Larmor angular frequency oj of the ground-state atoms. This precession does not last indefinitely for after a mean time x the orientation of the atom is destroyed by a collision or by absorption of another photon. In order to... 

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