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Answer :
The sample is approximately 74 minutes old. The correct option is A.
To find out how old the sample is, we need to use the formula for half-life which suggests that after each half-life, half of the remaining radioactive atoms will have decayed.
In this case, Lead-196 has a half-life of 37 minutes, and we are starting with a sample that currently has 20 atoms of lead-196 and 60 atoms of thallium-196. We can infer that the original sample must have started with 80 atoms of lead-196 to have decayed to the current ratio (since for every 20 atoms of lead decaying, we gain the same amount of thallium).
80 atoms → 40 atoms (1 half-life, 37 minutes),
40 atoms → 20 atoms (another half-life, another 37 minutes).
Thus, two half-lives have passed to go from 80 to 20 atoms of lead, which totals 74 minutes. Therefore, the correct answer is A. 74 minutes.
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