Has and decays by two channels: by emission and by electron capture

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radioactivity and decay modes

The Nucleus Resolved, Ch Decay rates from the golden rule: kinetics closed and alpha decay finished

Problem

^{22}\mathrm{Na}

has

T_{1/2}=2.6018\,\mathrm{y}

and decays by two channels:

90.3\%

\beta^+

emission and

9.7\%

by electron capture. Someone argues: "Since

90.3\%

of decays are

\beta^+

emission, the partial half-life for the

\beta^+

channel must be

90.3\%

of the total half-life:

T_{1/2,\beta^+}=0.903\times2.6018\,\mathrm{y}=2.35\,\mathrm{y}

." Find the error in this working, explain why the stated result cannot be right, and give the correct partial half-life for the

\beta^+

channel.