Chapter 18 - Nuclear Chemistry - Questions for Review and Thought - More Challenging Questions - Page 817f: 94

75.1 years.

$\frac{original\, activity}{present\,activity}=\frac{A_{0}}{A}=\frac{100}{1.45}$ Decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{12.3\,y}=0.05634\,y^{-1}$ $\ln(\frac{A_{0}}{A})=kt$ $\implies \ln(\frac{100}{1.45})=4.2336=(0.05634\,y^{-1})\times t$ $\implies t=\frac{4.2336}{0.05634\,y^{-1}}=75.1\,y$