( ) decays by positron emission to the ground state of ( ) with branching fraction…

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

The Nucleus Resolved, Ch Beta decay: Fermi's theory, parity violation and the double beta modes

Problem

^{11}\mathrm{C}

(

3/2^-

) decays by positron emission to the ground state of

^{11}\mathrm{B}

(

3/2^-

) with branching fraction essentially

100\%

and half-life

T_{1/2} = 20.36\,\mathrm{min}

. The atomic mass excesses are

\Delta(^{11}\mathrm{C}) = +10.649\,\mathrm{MeV}

and

\Delta(^{11}\mathrm{B}) = +8.668\,\mathrm{MeV}

. ((a)) Calculate

Q_{\beta^+}

, with the electron count made explicit. ((b)) Using the approximation

f \approx W_0^5/30

with

W_0 = 1 + Q_{\beta^+}/m_ec^2

(treated here as a rough estimate, since

Q_{\beta^+}

is only a few times

m_ec^2

), estimate

f

ft

and

\log_{10}ft