- 4 Hydrogen Atom 10 If The Proton Is Approximated As A Uniform Charge Distribution In A Sphere Of Radius R Show That 1 (36.85 KiB) Viewed 50 times
4. Hydrogen atom (10) If the proton is approximated as a uniform charge distribution in a sphere of radius R, show that the shift of an s-wave atomic energy level in the hydrogen atom, from the value it would have for a point proton, is approximately 2π Ens ²e²|Vns (0)|²R²2 using the fact that the proton radius is much smaller than the Bohr radius. Why is the shift much smaller for non-s states? The 2s hydrogenic wave function is (2a)-3/2-1/2 (1-27) exp(-20). What is the approximate splitting (in eV) between the 2s and 2p levels induced by this effect? [ao 5 x 10 cm for H, R≈ 10-¹3 cm.]