A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h / e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( m is the mass of the electron)
B. h e 2 m
Magnetic moment aligned & M=I A=I ( r^2 ) \\ & M= ( e u 2 r ) ( r^2 ) aligned Given B ( r^2 )=n ( h e ) r ^2= h ~B e (2) ( n =1) And when charge moving in external magnetic field then r= m u q B v r = e ~B ~m (3) ( q =e) Put value from equation (2) and (3) in equation (1) aligned & M= ( e v 2 r ) ( r^2 ) \\ & M= e 2 ( e B m ) ( h B e ) \\ & M= e h 2 m aligned
Related: Physics — Magnetic Effects of Current · All PYQ Banks