At the end of 15 min, 1/32 of a sample of radioactive polonium remains. The corresponding half-life is:
Correct answer: D. 3 min
- A. 0.469 min
- B. 32 min
- C. 15 min
- D. 3 min
Explanation
The correct answer is 3 minutes. To determine this, we first need to understand the relationship between the half-life and the remaining fraction of the radioactive substance. After each half-life, the amount of the sample halves. Therefore, we can calculate how many half-lives have occurred in 15 minutes by examining the fraction that remains:Starting with 1 (the whole sample), after one half-life (3 min), we have 1/2 remaining; after two half-lives (6 min), we have 1/4 remaining; after three half-lives (9 min), we have 1/8 remaining; after four half-lives (12 min), we have 1/16 remaining; and after five half-lives (15 min), we have 1/32 remaining. This shows that 5 half-lives have occurred in 15 minutes, confirming that the half-life is indeed 3 minutes.Other options are incorrect as they do not result in 1/32 remaining after 15 minutes. For example, with a half-life of 15 minutes, only half of the sample would remain after 15 minutes (1/2), and with a half-life of 32 minutes, it would take much longer to reach 1/32 of the original sample.
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