Chapter 25 - Nuclear Chemistry - Example 25-3 - Using the Half-Life Concept and the Radioactive Decay Law to Describe the Rate of Radioactive Decay - Page 1121: Practice Example B

76 days

Decay constant $\lambda=\frac{0.693}{t_{1/2}}=\frac{0.693}{11.4\,d}=0.06079\,d^{-1}$ If original activity $A_{0}=100$, then Activity after time $t$, $A=1.0$ Recall that $\ln(\frac{A_{0}}{A})=\lambda t$ $\implies \ln(\frac{100}{1.0})=4.605=0.06079\,d^{-1}(t)$ $\implies t=\frac{4.605}{0.06079\,d^{-1}}=76\,d$