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EspañolGYROMAGNETIC RATIO
In physics, the 'gyromagnetic ratio' (also sometimes known as the 'magnetogyric ratio' in other disciplines) of a particle or system is the ratio of its magnetic dipole moment to its angular momentum. Its SI units are hertz per tesla (Hz/T), and it is often denoted by the symbol γ, gamma.
Consider a charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum on account of its rotation. It can be shown that as long as its charge and mass are distributed identically (e.g., both distributed uniformly), its gyromagnetic ratio is
:
where ''q'' is its charge and ''m'' is its mass. The derivation of this relation is as follows:
It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result follows from an integration. Suppose the ring has radius ''r'', area ''A'' = π''r''2, mass ''m'', charge ''q'', and angular momentum ''L''=''mvr''. Then the magnitude of the magnetic dipole moment is
:
as desired.
An isolated electron has an angular momentum and a magnetic moment resulting from its spin. While an electron's spin is sometimes visualized as a literal rotation about an axis, it is in fact a fundamentally different, quantum-mechanical phenomenon with no true analogue in classical physics. Consequently, there is no reason to expect the above classical relation to hold. In fact it does not, giving the wrong result by a dimensionless factor called the electron 'g-factor', denoted ''ge'' (or just ''g'' when there is no risk of confusion):
:
where ''μ''B is the Bohr magneton. The electron ''g''-factor ''ge'' is a bit more than two, and has been measured to twelve decimal places (Odom et al., 2006).
The electron gyromagnetic ratio is given by NIST NIST as
:
Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
:
where ''μ''p is the nuclear magneton, and ''g'' is the g-factor of the nucleon or nucleus in question.
The gyromagnetic ratio of a nucleus is particularly important because of the role it plays in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). These procedures rely on the fact that nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength.
Approximate values for some common nuclei are given in the Table below (Bernstein 2004).
★ Dirac Equation
★ Landé g-factor
★ NMR
★ Chemical shift
★ Larmor equation
★ Dirac Equation in Curved Spacetime -- On the Gyromagnetic Ratio
★ Marc Knecht, ''The Anomalous Magnetic Moments of the Electron and the Muon'', Poincaré Seminar (Paris, Oct. 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.) ; ''Poincaré Seminar 2002'', Progress in Mathematical Physics 30, Birkhäuser (2003), ISBN 3-7643-0579-7.
★ S.J. Brodsky, V.A. Franke, J.R. Hiller, G. McCartor, S.A. Paston, and E.V. Prokhvatilov, ''A nonperturbative calculation of the electron's magnetic moment'', ''Nuclear Physics'' 'B 703' (2004) 333.
★ Matt A. Bernstein, Kevin F. King, Xiaohong Joe Zhou, In: ''Handbook of MRI Pulse Sequences'', Publisher: Academic Press (September 7, 2004), Pages 960-1
★ B. Odom, D. Hanneke, B. D'Urso and G. Gabrielse, "New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron", Phys. Rev. Lett. '97', 030801 (2006).
| Contents |
| Gyromagnetic ratio for a classical rotating body |
| Gyromagnetic ratio for an isolated electron |
| Gyromagnetic ratio for a nucleus |
| See also |
| See also |
| References |
Gyromagnetic ratio for a classical rotating body
Consider a charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum on account of its rotation. It can be shown that as long as its charge and mass are distributed identically (e.g., both distributed uniformly), its gyromagnetic ratio is
:
where ''q'' is its charge and ''m'' is its mass. The derivation of this relation is as follows:
It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result follows from an integration. Suppose the ring has radius ''r'', area ''A'' = π''r''2, mass ''m'', charge ''q'', and angular momentum ''L''=''mvr''. Then the magnitude of the magnetic dipole moment is
:
as desired.
Gyromagnetic ratio for an isolated electron
An isolated electron has an angular momentum and a magnetic moment resulting from its spin. While an electron's spin is sometimes visualized as a literal rotation about an axis, it is in fact a fundamentally different, quantum-mechanical phenomenon with no true analogue in classical physics. Consequently, there is no reason to expect the above classical relation to hold. In fact it does not, giving the wrong result by a dimensionless factor called the electron 'g-factor', denoted ''ge'' (or just ''g'' when there is no risk of confusion):
:
where ''μ''B is the Bohr magneton. The electron ''g''-factor ''ge'' is a bit more than two, and has been measured to twelve decimal places (Odom et al., 2006).
The electron gyromagnetic ratio is given by NIST NIST as
:
Gyromagnetic ratio for a nucleus
Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
:
where ''μ''p is the nuclear magneton, and ''g'' is the g-factor of the nucleon or nucleus in question.
The gyromagnetic ratio of a nucleus is particularly important because of the role it plays in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). These procedures rely on the fact that nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength.
Approximate values for some common nuclei are given in the Table below (Bernstein 2004).
| Nucleus | γ / 2π (MHz/T) |
|---|---|
| 1H | 42.576 |
| 3He | -32.434 |
| 7Li | 16.546 |
| 13C | 10.705 |
| 14N | 3.0766 |
| 15N | -4.3156 |
| 17O | -5.7716 |
| 23Na | 11.262 |
| 31P | 17.235 |
| 129Xe | -11.78 |
See also
★ Dirac Equation
★ Landé g-factor
★ NMR
★ Chemical shift
★ Larmor equation
See also
★ Dirac Equation in Curved Spacetime -- On the Gyromagnetic Ratio
References
★ Marc Knecht, ''The Anomalous Magnetic Moments of the Electron and the Muon'', Poincaré Seminar (Paris, Oct. 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.) ; ''Poincaré Seminar 2002'', Progress in Mathematical Physics 30, Birkhäuser (2003), ISBN 3-7643-0579-7.
★ S.J. Brodsky, V.A. Franke, J.R. Hiller, G. McCartor, S.A. Paston, and E.V. Prokhvatilov, ''A nonperturbative calculation of the electron's magnetic moment'', ''Nuclear Physics'' 'B 703' (2004) 333.
★ Matt A. Bernstein, Kevin F. King, Xiaohong Joe Zhou, In: ''Handbook of MRI Pulse Sequences'', Publisher: Academic Press (September 7, 2004), Pages 960-1
★ B. Odom, D. Hanneke, B. D'Urso and G. Gabrielse, "New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron", Phys. Rev. Lett. '97', 030801 (2006).
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