The hydrogen ground-state hyperfine interval is

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 Hyperfine structure and isotope shifts

Problem

A_{\rm hfs}(1S_{1/2}) = 1420.4\,\mathrm{MHz}

. The Fermi contact term is proportional to the electron's contact density

|\psi_{n00}(0)|^2 = \dfrac{1}{\pi n^3 a_0^3}

. Using this scaling, predict

A_{\rm hfs}(3S_{1/2})

for hydrogen.

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