Question
The half-life of carbon-14 is 5730 years. How long will it take for the number of carbon- 14 nuclei in a sample to drop to a quarter of the original number?
Answer
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(302 Votes)
Gwenllian
Elite · Tutor for 8 years
Answer
11460 years (2 * 5730 years)
Explanation
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of Carbon-14 is given as 5730 years. This means that after 5730 years, half of the Carbon-14 nuclei in a sample will have decayed.If we want the number of Carbon-14 nuclei to drop to a quarter of the original number, we need to go through 2 half-life periods. This is because after one half-life, half of the original nuclei remain (1/2), and after another half-life, half of the remaining nuclei decay, leaving a quarter of the original nuclei (1/2 * 1/2 = 1/4).Therefore, to find out how long it will take for the number of Carbon-14 nuclei in a sample to drop to a quarter of the original number, we multiply the half-life of Carbon-14 by 2.