Question

${}^{6}4\text{Cu}$ (half-life = $12.8$hr) decays by ${\beta }^{-}$ emission ($38\%$),${\beta }^{+}$ emission ($19\%$) and electron capture ($43\%$). Write the decay product and calculate partial half-lives for each of the decay processes.

Answer 1

Let ${\beta }^{-}$ emission = ${\lambda }_1$
${\beta }^{+}$ emission = ${\lambda }_2$
$k-$electron emission = ${\lambda }_3$

${\lambda }_{net}={\lambda }_1+{\lambda }_2+{\lambda }_3$

Fractional yield of path (I) = $\frac{{\lambda }_1}{{\lambda }_{net}}=\frac{(t_{1/2}{)}_{net}}{(t_{1/2}{)}_1}$

Half life of path I = $\frac{(t_{1/2}{)}_1}{Fractionalyield}=\frac{12.8}{0.38}=33.684hr$

Half life of path II = $\frac{12.8}{0.19}=67.368hr$

Half life of path III = $\frac{12.8}{0.43}=29.767hr$