Show that the orbital magnetic dipole moment of a revolving electron is` evr//2. `

Explanation

Let, r, v and T be the orbital radius, speed and period of motion of the electron.
Then, `" "T=(2pir)/(v)`
The orbital motion of the electron constitutes a loop of conventional current I in the opposite sense of its revolution.
`I=(e)/(T)=(ev)/(2pir)`
So the magnetic dipole moment associated with this electronic current loop is given by
`M_(o)=IxxA=("ev")/(2pir)xxpir^(2)=(1)/(2)xxevr`
`implies" "=("evr")/(2)`