Gyromagnetic ratio

From Wikipedia, the free encyclopedia

Jump to: navigation,
search

In physics,
the magnetogyric ratio (more commonly called the gyromagnetic
ratio) 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.

Contents

1 Magnetogyric ratio for a
classical rotating body

2 Magnetogyric ratio for an
isolated electron

3 Magnetogyric ratio for a
nucleus

4 See also

5 References

[edit]
Magnetogyric 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 magnetogyric 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 = πr2, mass m,
charge q, and angular momentum L=mvr. Then the magnitude of
the magnetic dipole moment is

as desired.

[edit]
Magnetogyric 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 μB is the Bohr magneton. The
electron g-factor ge is a bit more than two, and has
been measured to twelve decimal places (Gabrielse, 2006).

The electron magnetogyric ratio is given by NIST [1]
as

[edit]
Magnetogyric 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 μp is the nuclear magneton, and
g is the g-factor of the nucleon or
nucleus in question.

The magnetogyric 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 magnetogyric 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

7Li

16.546

13C

10.705

14N

3.0766

15N

-4.3156

17O

-5.7716

23Na

11.262

31P

17.235

[edit]
See also

Landé g-factor

NMR

Chemical shift

Larmor equation

[edit]
References

Note
1: 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

^
NIST

Retrieved from "http://en.wikipedia.org/wiki/Gyromagnetic_ratio"

Category: Atomic
physics

Views

Article

Discussion

Edit
this page

History

Personal tools

Sign
in / create account

Navigation

Main
page

Contents

Featured
content

Current events

Random article

interaction

About Wikipedia

Community
portal

Recent
changes

Contact us

Make a donation

Help

Search

Toolbox

What
links here

Related
changes

Upload file

Special pages

Printable
version

Permanent
link

Cite
this article

In other languages

Deutsch

Italiano

Русский

Українська

This page was last modified 21:30, 13 April 2007.

All text is available under the terms of the GNU
Free Documentation License. (See Copyrights
for details.)
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a
US-registered 501(c)(3) tax-deductible
nonprofit charity.

Privacy policy

About Wikipedia

Disclaimers