The Spinning Particle Model
Gyromagnetic Ratio g=2
The gyromagnetic ratio of a particle or system is the ratio of its magnetic dipole moment to its angular momentum.
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Suppose we divide the classical spherical charged electron in rings. Each 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:
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But the measured experimental data is :
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With Gyromagnetic Ratio g=2 .
This means once more that our electron cannot have a classical sphere like structure.
This gyromagnetic ratio comes from the two-fold spin structure.
The spin is expressed in terms of the orbital motion of the CC around the CM and also of the rotation of the body frame.
The orbital motion quantizes with value 1.
The rotational motion quantizes with value ½ in the opposite direction, so that the total spin is ½ in the direction of the orbital angular momentum.
But the magnetic moment of the electron is related to the orbital part of its angular momentum with a normal g=1 relation but with g=2 when expressed in terms of the total spin S. (More Info)
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M. Rivas |