Chapter 25 - Nuclear Chemistry - Exercises - Self-Assessment Exercises - Page 1146: 89

(d) 5.00 d

Initial decay rate $R_{0}=2.00\times10^{10}\,s^{-1}$ Rate after time $t$, $R=6.25\times10^{8}\,s^{-1}$ Time $t=25.0\,d$ Recall that $\ln(\frac{R_{0}}{R})=kt=\frac{0.693}{t_{1/2}}\times t$ $\implies \ln(\frac{2.00\times10^{10}}{6.25\times10^{8}})=3.465736=\frac{0.693}{t_{1/2}}\times 25.0\,d$ Or $t_{1/2}=\frac{0.693\times25.0\,d}{3.465736}=5.00\,d$