For a sealed capsule containing a radioactive isotope Z, the mass of undecayed atoms remaining is tracked and plotted as a smooth curve of mass m(t) versus time t:
• m=160μg at t=0h
• m=113μg at t=2.5h
• m=80μg at t=5.0h
• m=57μg at t=7.5h
• m=40μg at t=10.0h
Assume the trend represents an ideal, single-isotope exponential decay.
(a) Determine the half-life of isotope Z from the plotted data.
(b) Predict the mass of undecayed isotope Z that will remain at t=15.0h. Show your reasoning.
(c) If the capsule originally contained 320μg of isotope Z at the time of manufacture, estimate how many hours before t=0 the capsule was filled. Clearly outline the steps you used to reach your estimate.