An electron in the ground state of hydrogen atom is revolving in anticlockwise direction in circular orbit of radius R. The orbital magnetic dipole moment of the electron will be

Explanation

The orbiting electron behaves as a current loop.The equivalent current ,`i=(net charge)/(time of revolution)=(e)/(f)=ef(rot)`.Now, magnetic diople moment `mu=niA`, n=number of the turns of the loop=1,A=area of the loop=`pi r^(2)`,`implies mu =(1)(ef_(rot)) (pi r^(2)) implies mu=pi er^(2) f_(rot)` putting the values of `f_(rot)` and r we obtain,`mu=pie((n^(2)h^(2)epsilon_(0))/(pime^(2)Z))((mZ e^(4)))/(4(epsilon)_(0)^(2)h^(3)n^(3)=(ehn)/(4pim)`