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Answer :
Final answer:
To find the percentage of decayed sample, divide the total time by the half-life to determine the number of half-lives, and then calculate the percentage of decay based on the number of half-lives.
Explanation:
To find the percentage of a sample that will have decayed after a certain time, we need to determine how many half-lives have passed. In this case, we are given that the half-life of 11C is 20.3 minutes, and we want to know the percentage decay after 1.69 hours (which is 101.4 minutes).
Since the half-life is 20.3 minutes, we can divide 101.4 minutes by 20.3 minutes to find the number of half-lives. This gives us 5 half-lives.
Each half-life corresponds to a decay of 50% of the original sample. Since 5 half-lives have passed, the percentage of the sample that will have decayed is 50% x 50% x 50% x 50% x 50% = 3.1%.
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