Answer
3.6 minutes.
Work Step by Step
Start with equation 30–5 for the activity.
$$R=\frac{1}{6}R_0=R_0e^{-\lambda t}$$
$$ \frac{1}{6}=e^{-\lambda t}$$
Combine this with equation 30–6, which relates the decay constant to the half-life.
$$ \frac{1}{6}= e^{-(ln\;2) t/T_{1/2}}$$
Now solve for the half-life.
$$ T_{1/2}=-\frac{ln\;2}{ln(R/R_0)}t$$
$$ T_{1/2}=-\frac{ln\;2}{ln(1/6)}(9.4m)=3.6m$$
