To find out how many days a scientist would need to wait for the radioactivity of Manganese-52 to be 12.5% of the starting amount, we can use the half-life of the isotope.
The half-life of Manganese-52 is 6 days. This means that after every 6 days, the quantity of the substance reduces to half of its previous amount.
Starting amount: 100%
After the first half-life (6 days): 50% After the second half-life (12 days): 25% After the third half-life (18 days): 12.5%
Thus, it takes 3 half-lives for the radioactivity to reach 12.5% of the original amount. Since each half-life is 6 days, the total time is:
3 half-lives × 6 days/half-life = 18 days.
Therefore, the scientist would have to wait 18 days for the radioactivity to be 12.5% of the starting amount.
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