For hydrogen with

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

Reading the Spectrum, Ch The Coulomb spectrum from wave mechanics: quantum numbers and degeneracy

Problem

For hydrogen with l=0l=0, a trial energy of E=−12.0 eVE=-12.0\,\mathrm{eV} is substituted into the radial equation and the solution u(r)u(r) that vanishes at r=0r=0 is followed out to large rr. Predict what u(r)u(r) does as r→∞r\to\infty, and explain why, given that hydrogen's l=0l=0 energies are En=−13.6 eV/n2E_n=-13.6\,\mathrm{eV}/n^2 (n=1,2,3,…n=1,2,3,\ldots).

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