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The Larmor frequency is important in NMR spectroscopy. The gyromagnetic ratios, which give the Larmor frequencies at a given magnetic field strength, have been measured and tabulated. [3] Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction.
This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from Greek: γύρος, "turn") property (i.e. angular momentum), it is also, at the same time, a ratio between the ...
The geomagnetic field strength and hence precession frequency varies with location and time. Larmor precession frequency = magnetogyric ratio x magnetic field Proton magnetogyric ratio = 42.576 Hz/μT (also written 42.576 MHz/T or 0.042576 Hz/nT) Earth's magnetic field: 30 μT near Equator to 60 μT near Poles, around 50 μT at mid-latitudes.
Taking for example the H 2 O molecules in liquid phase without the contamination of oxygen-17, the value of K is 1.02×10 10 s −2 and the correlation time is on the order of picoseconds = s, while hydrogen nuclei 1 H at 1.5 tesla precess at a Larmor frequency of approximately 64 MHz (Simplified. BPP theory uses angular frequency indeed).
The Larmor formula can only be used for non-relativistic particles, which limits its usefulness. The Liénard-Wiechert potential is a more comprehensive formula that must be employed for particles travelling at relativistic speeds. In certain situations, more intricate calculations including numerical techniques or perturbation theory could be ...
The operating (or Larmor) frequency of a magnet (usually quoted as absolute value in MHz) is calculated from the Larmor equation [4] =, where B 0 is the induction of the magnet (SI units of tesla), and is the magnetogyric ratio of the nucleus — an empirically measured fundamental constant determined by the details of the structure of each nucleus.
The Larmor frequency can be determined from the product of the gyromagnetic ratio with the magnetic field strength. Since for the neutron the sign of γ n is negative, the neutron's spin angular momentum precesses counterclockwise about the direction of the external magnetic field.
These g-factors may be multiplied by 7.622 593 285 (47) MHz/T, [7] which is the nuclear magneton divided by the Planck constant, to yield Larmor frequencies (in MHz/T). If divided instead by the reduced Planck constant, which is 2π less, a gyromagnetic ratio expressed in radians is obtained, which is greater by a factor of 2π.