The magnetic moment vectors `mu_(s) and mu_(l)` 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 :
`overset(to)(mu_(s) ) = -((e)/(m)) S, overset(to)(mu_(l)) = - ((e)/( 2m)) overset(to)(l)`
Which of these relations is in accordance with the result expected classically ? Outline the derivation of the classical result.

Explanation

According to classical physics due to orbital motion of electron around the nucleus, it has orbital angular momentum `overset(to) (l) ` and orbital magnetic moment `overset(to) (mu_(l ) )`, related by following relation.

According to quantum physics, alongwith orbital motion, electron also has spinning , motion around its axis. Due to such motion, electron has spin magnetic moment `overset(to) (mu_(s) )` which is given by following relation.
`overset(to) (mu_(s ) ) = - ((e)/( m) ) overset(to) (S) " "...(2)`
where `overset(to) (S) = ` spin angular momentum of electron.
Above relation is verified experimentally, which shows a great success of quantum theory.