In hydrogen atom, an electron of charge a revolves in a orbit radius r with speed v. Then, magnetic moment associated with electron is

Step-by-step solution

Magnetic moment of revolving electron, μ e = i × A where, i = current and A = area, μ e = e T × π r 2 (As current, i = c u r r e n t t i m e = e t ) where, T = time period of revolution and r = radius of orbit. μ e = e 2 π r × v × π r 2 ∵ T i m e p e r i o d T = d i s t a n c e s p e e d where, v = velocity of revolving electron ⇒ μ e = e v r 2 Hence, the magnetic moment of revolving electron is e v r 2