A fossilized leaf contains 21% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.
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To determine the age of the fossil, we can use the concept of carbon dating. Carbon 14 is an isotope of carbon that decays over time at a known rate. The half-life of carbon 14 is 5600 years, which means that after 5600 years, half of the original carbon 14 would have decayed.
In this case, the fossilized leaf contains 21% of its normal amount of carbon 14. This means that 79% of the carbon 14 has decayed, because the remaining 21% is what is left.
We can use the formula for exponential decay to find the age of the fossil:
Age = (t1/2) * log(Nt / N0)
Where:
- Age is the age of the sample
- t1/2 is the half-life of the isotope (5600 years in this case)
- Nt is the remaining amount of the isotope
- N0 is the initial amount of the isotope
In this case, we know that Nt is 21% of the normal amount, which means it is 0.21, and N0 is 1 (the original amount).
Plugging these values into the formula:
Age = (5600) * log(0.21 / 1)
Calculating this using a calculator or math software, we find:
Age ≈ 4769 years
Therefore, the fossil is approximately 4769 years old (to the nearest year).
just find t where
(1/2)^(t/5600) = 0.21