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

Explanation

The magnetic dipole moment of a rovolving electron:The electron of charge `(-e)` per form unifrom s circular motion around motion around a stationary heavy nucleus of charge `+Ze`.This constitutes a current `I`
`therefore 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`
Substituting the value of `T` in (i), we get
`I=(e/(2pir))/upsilon=(ev)/(2pir)`
The magnetic moment `(mul)` associated with this circular current is
`mul=I pir^(2) [becausevecm=IvecA]`
`thereforemul=(ev)/(2pir).pir^(2)=(evr)/2`
The direction of this magnetic moment is into the plane of the paper.