The magnetic moment vectors μs and μl 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 be given by:
μs = – (e/m) S,
μl = – (e/2m)l
Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.
We know,
It follows from the definition of μ1 and l.
μ1 = i × A = 
l = mvr = m
Where, r is the radius of the circular path traced by the electron around the nucleus, with the mass of electron m and charge (-e) and time period T.
Divide the above equations-
⇒ 
⇒ 
Clearly μ1 and l will be antiparallel.
On the other hand, 
is obtained on the basis of quantum mechanics.