Charcoal from an ancient campfire has a ratio of 14C to 12C that is one- fourth that of new wood. About how old is the charcoal? The half- life of 14C is 5730 years.

Charcoal from an ancient campfire has a ratio of 14C to 12C that is one-sixteenth that of new wood. About how old is the charcoal? The half-life of 14C is 5730 years.

To determine the age of the charcoal, we can use the concept of carbon dating. Carbon dating relies on the fact that carbon-14 (14C) is a radioactive isotope of carbon that decays over time. The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the original amount of carbon-14 in a sample will have decayed.

Now, let's approach the problem step by step:

1. First, we need to understand the meaning of the ratio of 14C to 12C in the charcoal. The ratio being one-fourth that of new wood means that the proportion of carbon-14 in the charcoal is one-fourth of the proportion in new wood.

2. Knowing the concept of half-life, we can deduce that every half-life (5730 years), the amount of carbon-14 is halved. So, if the ratio in the charcoal is one-fourth that of new wood, it means that the charcoal has gone through two half-lives (0.5 * 0.5 = 0.25).

3. To find the age of the charcoal, we need to determine how many half-lives have passed. Since we know the ratio is one-fourth, the amount of carbon-14 remaining in the charcoal is one-fourth of the original amount. Therefore, we have gone through two half-lives.

4. We can calculate the age of the charcoal by multiplying the half-life (5730 years) by the number of half-lives. In this case, 2 * 5730 = 11,460 years.

Therefore, the charcoal is approximately 11,460 years old.

if 1/4 remains, that means 2 half-lives have passed.

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