Isotope Z undergoes radioactive decay with a half-life of

CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

2.4\,\text{years}

. A sealed source initially contains

3.0\,\text{mg}

of pure Z. (a) Determine the decay constant of isotope Z in

\text{s}^{-1}

. Show your reasoning. (b) After precisely

5.0\,\text{years}

have elapsed, calculate the mass of isotope Z that remains undecayed in the source. (c) Estimate how much additional time, beyond the first

5.0\,\text{years}

, must pass before the mass of isotope Z in the source decreases to

0.25\,\text{mg}

. Provide your answer in years and explain each step of your solution.