Deduce an expression for the magnetic dipole moment of an electron orbiting around the central nucleus.

Explanation

The magnetic dipole moment of revolving electron: The electron of charge `(-e)` perform uniforms cicular motion around a stationary heavy nucleus of charge `+Ze`. This constitutes a current `I`.

`:. I =(e )/(T)`.....(i)
where `T` is the time period of revolution. Let `r` be the orbital radius of electron and `v` the orbital speed. Then
`T=(2pir)/(upsilon)`.....(ii)
The magnetic moment `(mu l)` associated with this circular is into the plane of the paper.