A level has a measured total half-life

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radioactivity and decay modes

The Nucleus Resolved, Ch Gamma decay: multipoles, isomers, internal conversion and the Mossbauer line

Problem

100\,\mathrm{keV}

level has a measured total half-life

T_{1/2}=3.2\,\mathrm{ns}

. Tables give the total internal-conversion coefficient for this transition as

\alpha_{\rm IC}=3.0

. Someone argues: "The half-life tells us directly how fast the level empties out by photon emission, so the photon partial rate is

\lambda_\gamma=\frac{\ln 2}{T_{1/2}}=\frac{0.693}{3.2\,\mathrm{ns}}=2.17\times10^{8}\,\mathrm{s^{-1}}."

((a)) Find the error in this reasoning. ((b)) Give the correct photon partial decay rate and the corresponding photon partial mean life.