Answer
1.2 hours.
Work Step by Step
Start with equation 30–5 for the activity.
$$R=R_0e^{-\lambda t}$$
Combine this with equation 30–6, which relates the decay constant to the half-life.
$$R=R_0e^{-\lambda t}= R_0e^{-(ln\;2) t/T_{1/2}}$$
Now solve for the half-life.
$$ T_{1/2}=-\frac{ln\;2}{ln(R/R_0)}t$$
$$ T_{1/2}=-\frac{ln\;2}{ln(140/1120)}(3.6h)=1.2h$$
