If a bone is found to have 20% of its normal amount of carbon 14, how old is the bone?
To determine the age of the bone, we need to use the concept of carbon dating. Carbon dating relies on the fact that carbon-14 (C-14) is a radioactive isotope that decays over time.
The half-life of carbon-14 is approximately 5730 years, which means that after this time, half of the carbon-14 in a sample will have decayed.
If we assume that the bone initially had its normal amount of carbon-14, then after one half-life (5730 years), the bone would have 50% of its original carbon-14 remaining.
Since the bone was found to have only 20% of its normal amount of carbon-14, we can use this information to calculate the approximate age.
Let's denote the number of half-lives as 'n'.
Given that the bone has 20% of its original carbon-14, it means that it has gone through four half-lives (50% * 50% * 50% * 50% = 0.20 or 20%).
To find the age, we multiply the number of half-lives (n) by the half-life of carbon-14 (5730 years):
n * 5730 years = 4 * 5730 years = 22,920 years
Therefore, based on the 20% remaining carbon-14, the bone is approximately 22,920 years old.
To determine the age of the bone based on its carbon-14 content, we can use a technique called carbon dating. Carbon dating relies on the fact that carbon-14 is a radioactive isotope that undergoes decay over time at a known rate.
The first step is to understand the concept of a half-life. The half-life of carbon-14 is approximately 5730 years, which means that it takes 5730 years for half of the carbon-14 in a sample to decay. This decay continues at a steady rate, so the amount of carbon-14 remaining in a sample decreases exponentially over time.
Now, let's calculate the age of the bone using the given information. If the bone has only 20% of its normal amount of carbon-14, it means that 80% of the carbon-14 has decayed. This corresponds to one half-life, as each half-life reduces the amount of carbon-14 by 50%.
To find the number of half-lives that have elapsed, we can use the formula:
(number of half-lives) = ln (remaining amount of carbon-14 / initial amount of carbon-14) / ln(0.5)
In this case:
(number of half-lives) = ln (0.20) / ln(0.5) ≈ 1.386 / 0.693 ≈ 2
Therefore, 2 half-lives have elapsed. Since each half-life is approximately 5730 years, we can multiply the number of half-lives by the half-life duration to find the age of the bone:
(age of the bone) = (number of half-lives) x (duration of a half-life)
(age of the bone) = 2 x 5730 years ≈ 11,460 years
Hence, the bone is estimated to be around 11,460 years old.