The difference between the 2P3/2 and 2P1/2 doublet in hydrogen due to the spin-orbit spl...

The difference between the 2P_3/2 and 2P_1/2 doublet in hydrogen due to the spin-orbit splitting is 4.5 × 10^-5 eV. (a) Compare this with the potential energy given in the preceding problem. (b) Compare this with a more complete calculation giving the potential energy as

where α is the fine-structure constant, α 1/137.