An electron moving around the nucleus with an angular momentum L has a magnetic moment ( e= charge on electron, m= mass of electron )

Step-by-step solution

The magnetic moment of a current carrying coil is given by: =i A=i r^2 The moving electron in an orbit is equivalent to a coil with current i= e T , where T is the period of rotation around the nucleus. Therefore, = e T r^2 Using definition of angular momentum L=m v r or r= L m v and the velocity of the electron is given by v= 2 r T or 1 T = v 2 r We can substitute r and 1 ~T into the expression for magnetic moment, =e ( v 2 r ) r^2= e v 2 r= e v 2 L m v = ( e 2 m ) L