Consider an electron revolving around a nucleus in an atom. Since the electron is a negatively charged particle, so atom will act as a current-carrying loop and its magnetic dipole moment is given by \\\\( M=lA \\\\)Where \\\\( l\\\\) =current and \\\\( A \\\\) =area of cross-sectionif \\\\( r \\\\) is the radius of orbit then\\\\( M=\\left( \\frac { e }{ t } \\right) \\left( \\pi r^{ 2 } \\right) \\\\)=\\\\( \\frac { e }{ \\frac { 2\\pi r }{ v } } \\pi r^2=\\frac{evr}{2} \\\\)Sice \\\\( mvr\\\\) = angular momentum \\\\( (L) \\\\)So, \\\\( M=\\left( \\frac { 2 }{ 2m_{ e } } \\right) L \\\\) (in vector form), since magnetic dipole moment of the electron and angular momentum are in opposite direction.