Carbon-14 has a half-life of 5730 yr. A living organism has an activity of 15.2 counts per minute (cpm)per gram of carbon. If a bone is determined to have an activity of 1.90 cpm per gram of carbon, how old is the bone?

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Quizplus · Accepted Answer

The activity of carbon-14 decreases over time as it decays. The half-life of carbon-14 is 5730 years, meaning every 5730 years, the activity is halved. To find out how many half-lives have passed for the activity to decrease from 15.2 cpm to 1.90 cpm, we can use the formula: $ \text{Number of half-lives} = \frac{\log(\text{final activity} / \text{initial activity})}{\log(0.5)} $. Plugging in the values, we get $ \frac{\log(1.90 / 15.2)}{\log(0.5)} \approx 3 $. Therefore, the bone is approximately 3 half-lives old, which is $ 3 \times 5730 $ years = 17,190 years, rounding to the nearest hundred gives 17,200 years.

Carbon-14 Has a Half-Life of 5730 Yr