Define and explain the gyromagnetic ratio and Landé g-factor, stating their physical importance.
The gyromagnetic ratio is defined as the ratio of the magnetic moment ( \vec{\mu} ) of a particle to its angular momentum ( \vec{J} ). Mathematically, it is expressed as: [ \gamma = \frac{\mu}{J} ] For an electron with orbital angular momentum ( \vec{L} ), the magnetic moment is given by [ \vec{\mu}_L = -\frac{e}{2m} \vec{L} ] where ( e ) is the charge of the electron and ( m ) its mass. The _______ _____ ____ ________ _____ ________ _____ ____ ______ __________.
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