If the angular momentum of an electron is $\vec J$ then the magnitude of the magnetic moment will be
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As we know for circulating electron magnetic moment
$M\,\,=\,\,\frac {1}{2}\,\,evr$ $ ....(i)$
and angular momentum $J\,\,=\,\, mvr$ $ ....(ii)$
From equation $(i)\,\,$ and $\,\,(ii),$ $M\,\,=\,\,\frac {eJ}{2m}$
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