Gyromagnetic ratio: Difference between revisions

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==Theory and experiment==
==Theory and experiment==
The relativistic quantum mechanical theory provided by the [[Dirac equation]] predicted the electron to have a magnetic moment of exactly two Bohr mangetons, where the Bohr magneton is:
The relativistic quantum mechanical theory provided by the [[Dirac equation]] predicted the electron to have a magnetic moment of exactly two Bohr mangetons, where the Bohr magneton is:<ref name=NIST4>


:<math>\mu_B = \frac{e \hbar }{2 m_e c } = \mathrm{0.9274 \times 10^{-24}\ J/T}\ , </math>
{{cite web |title=Bohr magneton |work=Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?eqmub|search_for=Bohr+magneton |publisher=NIST |accessdate=2011-03-28}}


with ''c'' the [[speed of light]] in ideal vacuum, and ''e'' the [[elementary charge]].
</ref>
 
:<math>\mu_B = \frac{e \hbar }{2 m_e } = \mathrm{927.400 915 \times 10^{-26}\ J/T}\ , </math>
 
with ''e'' the [[elementary charge]].


Subsequently (in 1947) experiments on the [[Zeeman effect|Zeeman splitting]] of the gallium atom in magnetic field showed that was not exactly the case, and subsequently this departure was calculated using [[quantum electrodynamics]].<ref name= Marciano>
Subsequently (in 1947) experiments on the [[Zeeman effect|Zeeman splitting]] of the gallium atom in magnetic field showed that was not exactly the case, and subsequently this departure was calculated using [[quantum electrodynamics]].<ref name= Marciano>

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The gyromagnetic ratio (sometimes magnetogyric ratio), , is the constant of proportionality between the magnetic moment (μ) and the angular momentum(J) of an object:

Its SI units are radian per second per tesla (s−1·T -1) or, equivalently, coulomb per kilogram (C·kg−1). When the object is placed in a magnetic flux density B, because of its magnetic moment it experiences a torque and precesses about the field.

Examples

The electron gyromagnetic ratio is:[1]

where μe is the magnetic moment of the electron (-928.476 377 x 10-26 J T-1), and ℏ is Planck's constant divided by 2π and ℏ/2 is the spin angular momentum.

Similarly, the proton gyromagnetic ratio is:[2]

where μp is the magnetic moment of the proton (1.410 606 662 x 10-26 J T-1). Other ratios can be found on the NIST web site.[3]

Theory and experiment

The relativistic quantum mechanical theory provided by the Dirac equation predicted the electron to have a magnetic moment of exactly two Bohr mangetons, where the Bohr magneton is:[4]

with e the elementary charge.

Subsequently (in 1947) experiments on the Zeeman splitting of the gallium atom in magnetic field showed that was not exactly the case, and subsequently this departure was calculated using quantum electrodynamics.[5]

Notes

  1. Electron gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
  2. Proton gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
  3. A general search menu for the NIST database is found at CODATA recommended values for the fundamental constants. National Institute of Standards and Technology. Retrieved on 2011-03-28.
  4. Bohr magneton. Fundamental physical constants. NIST. Retrieved on 2011-03-28.
  5. An historical summary can be found in Toichiro Kinoshita (2010). “§3.2.2 Early tests of QED”, B. Lee Roberts, William J. Marciano, eds: Lepton dipole moments. World Scientific, pp. 73 ff. ISBN 9814271837.  An introduction to the behavior of the electron in a magnetic flux is found in Yehuda Benzion Band (2006). “§5.1.1 Electron spin coupling”, Light and matter: electromagnetism, optics, spectroscopy and lasers. Wiley, pp. 297 ff. ISBN 0471899313.