Answer :
Final answer:
The half-life of a radioactive substance is the time required for half the atoms in the sample to decay. Given that a sample of a substance decreases from 6.80 mg to 2.50 mg over 57.3 years, it's apparent that slightly less than two half-lives have passed in that period. Consequently, the half-life of this substance is approximately 28.6 years.
Explanation:
The problem in question pertains to the concept of radioactive decay and the half-life of a substance. The half-life is defined as the time required for half the atoms in a radioactive sample to decay. It can be calculated by dividing the total time by the number of half-lives within that time span.
In this case, we start with 6.80 mg of a radioactive substance and end with 2.50 mg over a period of 57.3 years. Since this is a reduction by a factor of more than 2 (roughly 2.72 times), it indicates that more than one but less than two half-lives have occurred. Basically, it indicates that slightly less than two half-lives have passed in the 57.3 years.
Therefore, if we divide 57.3 years by let's say, approximately 2, we get the half-life of the substance to be around 28.6 years (Option 2), which is the correct answer.
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