The magnetic moment vectors `mu_s and mu_i` associated with the intrinsic spin angular momentum S and orbital angular momentum l, respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy ) to the given by

Explanation

`mu_i` is in accordance with classical theory. It follows from the definitions of `mu_f and l`
`mu_i=IA=(e/T)pir^2" "l=mvr=m(2pir^2)/T`
where r is the radius of the circular orbit which the electron of mass m and charge (-e) completes in time T. Clearly , `mu_i/l=e/(2m)`
Since charge of electron is negative (=-e) , it is easily seen the `1//4` and l are antiparallel,
Therefore , `mu_i=-(e/(2m))` INote `mu_s/S` in contrast to `mu_l/l` is `e/m` . i.e, twice the classically expected value . This latter result (verified experimentally ) is an outstanding consequence of modern theory (verified experimentally ) is an outstanding consequence of modern quantum theory and cannot be obtained classically .