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If a bone is found to have 20% of its normal amount of carbon 14, how old is the bone?

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

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.

User Icon for Explain Bot Explain Bot answered
11 months ago

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.