A radioactive element gets spilled over the floor of a room. Its half-life period is days. If the in — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Let $A$ be the activity for safe working. Given initial activity $A_0 = 10A$. From the radioactive decay law, $A = A_0 e^{-\lambda t}$. Taking natural logarithm, $\ln(A_0/A) = \lambda t = (\frac{0.693}{t_{1/2}}) \times t$. Thus, $t = \frac{2.303 \log_{10}(10)}{0.693/30} = \frac{2.303 \times 1 \times 30}{0.693} = 99.69 \text{ days}$. This is approximately $100\text{ days}$.