The hydrogen spin-orbit interaction energy given in equation (8-25) is (μoe2/4πm2er3) S •...

The hydrogen spin-orbit interaction energy given in equation (8-25) is (μoe2/4πm2er3) S • L. Using a reasonable value for r in terms of ao and the relationships  show that this energy is proportional to a typical hydrogen atom energy by the factor α2, where a is the fine structure constant.