The mean lives of a radioactive substance are 1620 years and 405 years for -emission and -emission, — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

The total decay constant $\lambda_{total} = \lambda_\alpha + \lambda_\beta = \frac{1}{1620} + \frac{1}{405} = \frac{1+4}{1620} = \frac{5}{1620} = \frac{1}{324} \text{ yr}^{-1}$. A decay of 3/4 leaves 1/4 of the sample, which corresponds to 2 half-lives. The effective half-life is $t_{1/2} = \frac{\ln 2}{\lambda_{total}} \approx 324 \times 0.693 = 224.532 \text{ yrs}$. Time required = $2 \times 224.532 = 449.06 \text{ yrs}$. Therefore, correct answer is 0449.