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

Explanation

In the Bohr model of the hydrogen atom, the electron of charge -e, revolves around the positively charged nucleus in a uniform circular motion. Let r, v and T be the orbital radius, speed and period of motion of the electron . Then,
`T=(2pi r)/(v) " " ` ...(1)
The orbital motion of the electron constitutes a loop of conventional current `I` in the opposite sense of its revolution.
`I=(e)/(T)=(ev)/(2pi r) " " ` ...(2)
Therefore, the magnetic dipole moment associated with this electronic current loop has a magnitude
`M_(0)="current" xx "area of the loop" `
`=I(pi r^(2))=(ev)/(2pi r) xx pi r^(2) =(1)/(2) evr " " ` ...(3)