A classical derivation is presented for magnetic x-ray scattering from
electronic orbital angular momentum. The orbital magnetic scattering
factor is identical to that for spin angular momentum, except for the
difference in gyromagnetic ratios. Unlike the spin result, which had p
reviously been obtained from both a classical Lagrangian and from quan
tum mechanics, the classical orbital scattering disagrees with quantum
mechanics and with available data. This disagreement between classica
l and quantum-mechanical results is present for the scattering from a
free electron in motion, scattering from an ideal current loop, as wel
l as for scattering from atomic orbital angular momentum.