PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure
The Structure of Quantum Mechanics, Ch Hydrogen, and the symmetry that explains it
Problem
For a hydrogen electron in the n=5 level:
((a)) Estimate v/c using v/c≈αfs/n, with αfs≈1/137.
((b)) Estimate the absolute size of the leading relativistic correction to E5, using the fact that such corrections are of relative order (v/c)2 of the level energy.
((c)) State, with a one-line reason, whether the non-relativistic treatment is more or less trustworthy at n=5 than at n=1.