Hydrogen is treated as a one-electron hydrogenic atom with a point

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Deriving the Spectrum, Ch Fine structure and the Lamb shift

Problem

Hydrogen is treated as a one-electron hydrogenic atom with a point, infinitely massive nucleus (reduced-mass corrections ignored). Using ⟨Hrel⟩=−En22mc2[4nl+12−3],\langle H_{\rm rel}\rangle = -\frac{E_n^2}{2mc^2}\left[\frac{4n}{l+\tfrac12}-3\right], with mc2=511 000 eVmc^2 = 511\,000\,\mathrm{eV} the electron rest energy and En=−13.6 eV/n2E_n = -13.6\,\mathrm{eV}/n^2, calculate the relativistic kinetic-energy correction ⟨Hrel⟩\langle H_{\rm rel}\rangle for the hydrogen 3d3d state (n=3n=3, l=2l=2). Give the result in μeV\mu\mathrm{eV}.

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