show that the electron revolving around the nucleus in a radius 'r' with orbital speed 'v' has magnetic moment evr/2.

Consider an atom in which an electron is revolving in a circular orbit of radius r around a positively charged nucleus. Suppose it is revolving in the counter-clockwise direction. The motion of this electron constitutes an electric current I in the clockwise direction.
Now, I= $\frac{e}{T}$
 where e is the magnitude of the charge on an electron and T is the period of revolution of the electron. If ω is the angular velocity of the revolving electron, then:-
   I= $\frac{e}{2\pi /\omega }$= $\frac{e\omega }{2\pi }$
Magnetic moment of current loop, M= I X A    
Where A is the face area of the orbit.
Now,          M = I x πr2
                      = $\frac{e\omega }{2\pi }$x πr2
                       = $\frac{e\omega r^2}{2}$
 Thats why,  M= $\frac{evr}{2}$     where v is the velocity of the electron.