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If the half-life of an isotope is 5 years, what fraction remains after 15 years?

  1. 1/2

  2. 1/4

  3. 1/8

  4. 1/16

The correct answer is: 1/8

To determine the fraction of an isotope that remains after a given period, we apply the concept of half-life, which is the time it takes for half of the substance to decay. In this scenario, the half-life of the isotope is 5 years. After 5 years, half of the original amount remains; therefore, we can express this as 1/2 of the original amount. After another 5 years (which totals 10 years), half of the remaining amount decays again. So, if we take the 1/2 that was left after the first 5 years, half of that is 1/4 of the original amount remaining after 10 years. After yet another 5 years (totaling 15 years), we take the 1/4 that remains and again halve it. Thus, half of 1/4 is 1/8 of the original amount left after 15 years. Hence, after 15 years, the fraction of the isotope that remains is calculated to be 1/8 of the original amount. This is why that answer is correct.