Question

If the half-life of a radioactive element is $12.5$ hours, then the time taken to disintegrate $256~g$ of the substance into $1~g$ is (in hours)

• A. $12.5$
• B. $25$
• C. $37.5$
• D. $100$

Hint:

Use the property that after $n$ half-lives, the quantity reduces by $2^n$ times.

Answer 1

The Correct Option is D

- The number of half-lives ($n$) required to reduce $256~g$ to $1~g$ is found by:
\[ \left(\frac{1}{2}\right)^n = \frac{1}{256} \] Since $256 = 2^8$, it implies:
\[ n = 8 \] - Each half-life is $12.5$ hours, so total time ($t$) is:
\[ t = n \times \text{half-life} = 8 \times 12.5 = 100~\text{hours} \] Thus, it takes 100 hours for the substance to reduce from 256 g to 1 g.