JAMB Chemistry 2024 Paper

Concept:After $n$ half-lives, the fraction of a radioactive substance remaining is $\left(\frac{1}{2}\right)^n$.Explanation:The total time elapsed is $10$ minutes.The half-life of the substance is $2$ minutes.So the number of half-lives that have passed is:$$n = \frac{10}{2} = 5$$The fraction remaining after $5$ half-lives is:$$\left(\frac{1}{2}\right)^5 = \frac{1}{32}$$Since the original mass is $1\text{ g}$, the residual mass is:$$\frac{1}{32}\text{ g}$$If the question strictly asks for the fraction disintegrated, it would be:$$1 - \frac{1}{32} = \frac{31}{32}$$However, $\frac{31}{32}$ is not among the options given.Therefore, among the options provided, $\frac{1}{32}$ is the fraction remaining.Answer:Option D: $\frac{1}{32}$ (fraction remaining).