MCAT Physics Question 131: Answer and Explanation
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Question: 131
11. Element X is radioactive and decays via α decay with a half-life of four days. If 12.5 percent of an original sample of element X remains after n days, what is the value of n?
- A. 4
- B. 8
- C. 12
- D. 16
Correct Answer: C
Explanation:
Because the half-life of element X is four days, 50 percent of an original sample remains after four days, 25 percent remains after eight days, and 12.5 percent remains after 12 days. Therefore, n = 12 days. Another approach is to set
where x is the number of half-lives that have elapsed. Solving for x gives x = 3. Thus, 3 half-lives have elapsed, and because each half-life is four days, we know that n = 12 days.