To determine how long a scientist would need to wait for the radioactivity of Manganese-52 to decrease to 12.5% of its original amount, we can follow these steps:
1. Understand the concept of half-life:
- Half-life is the time required for a quantity to reduce to half its initial amount. For Manganese-52, this time is 6 days.
2. Determine the fraction of the original amount after a certain number of half-lives:
- After 1 half-life (6 days), 50% of the original amount remains.
- After 2 half-lives (12 days), [tex]\(50\% \times 50\%\)[/tex] = 25% of the original amount remains.
- After 3 half-lives (18 days), [tex]\(25\% \times 50\%\)[/tex] = 12.5% of the original amount remains.
3. Confirming the result:
- We see that after 3 half-lives, the amount remaining is exactly 12.5% of the original amount. Since the half-life of Manganese-52 is 6 days, 3 half-lives equate to [tex]\(6 \text{ days} \times 3 = 18 \text{ days}\)[/tex].
Thus, the scientist would need to wait for 18 days for the radioactivity of Manganese-52 to decrease to 12.5% of the starting amount.
The correct answer is:
18 days
