A radioactive element spills over the floor. Its half-life period is exactly . If its initial activi — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Let safe activity be $A$. Initial activity $A_0 = 10A$. From decay law: $A = A_0 e^{-\lambda t} \Rightarrow \ln(A_0/A) = \lambda t$. Thus, $\ln(10) = (0.693 / 30) \times t$. Solving for $t$: $t = (2.303 \times 1 \times 30) / 0.693 = 99.69\text{ days} \approx 100\text{ days}$.