# 5.25) The magnetic moment vectors  and  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: Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

We know,

is in expected from classical physics.

Now, Magnetic moment associated with the orbital motion of the electron is:

= Current x Area covered by orbit = I x A

And, l = angular momentum = mvr

=

(m is the mass of the electron having charge (-e), r is the radius of the orbit of by the electron around the nucleus and T is the time period.)

Dividing these two equations:

, which is the same result predicted by quantum theory.

The negative sign implies that  and l are anti-parallel.

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