Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Title: Estimating the Age of a Fossil Using Carbon Dating**
**Introduction**
This section explains how to estimate the age of a fossil using the ratio of carbon isotopes. This method is based on the decay of radioactive carbon isotopes in once-living organic material.
**Understanding Carbon Isotopes**
In living organisms, the ratio of radioactive carbon isotopes to the total number of carbon atoms is approximately 1 to 10¹². Once the organism dies, these isotopes begin to decay at a known rate.
**The Formula**
The decay of carbon-14 isotopes can be modeled using the formula:
\[ R = 10^{-12} \left(\frac{1}{2}\right)^{\frac{t}{5715}} \]
- \( R \) is the ratio of carbon isotopes to carbon-14 atoms.
- \( t \) is the time in years since the organism died.
- The half-life of carbon-14 is about 5715 years.
**Example Calculation**
Suppose the given ratio \( R = 0.17 \times 10^{-12} \). Calculate the age of the fossil by solving for \( t \) using the provided formula.
**Conclusion**
This method allows scientists to determine the approximate age of a fossil by measuring carbon isotope ratios and applying the known decay laws.
**Input Box:**
[Enter the calculated age of the fossil in years, rounded to one decimal place.]
**yrs**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe68fb1ae-fc32-4d84-ad25-16ca36cebf4d%2F302074fa-b738-4db3-a1e1-57c2e7f39f11%2F7ijiii9_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Estimating the Age of a Fossil Using Carbon Dating**
**Introduction**
This section explains how to estimate the age of a fossil using the ratio of carbon isotopes. This method is based on the decay of radioactive carbon isotopes in once-living organic material.
**Understanding Carbon Isotopes**
In living organisms, the ratio of radioactive carbon isotopes to the total number of carbon atoms is approximately 1 to 10¹². Once the organism dies, these isotopes begin to decay at a known rate.
**The Formula**
The decay of carbon-14 isotopes can be modeled using the formula:
\[ R = 10^{-12} \left(\frac{1}{2}\right)^{\frac{t}{5715}} \]
- \( R \) is the ratio of carbon isotopes to carbon-14 atoms.
- \( t \) is the time in years since the organism died.
- The half-life of carbon-14 is about 5715 years.
**Example Calculation**
Suppose the given ratio \( R = 0.17 \times 10^{-12} \). Calculate the age of the fossil by solving for \( t \) using the provided formula.
**Conclusion**
This method allows scientists to determine the approximate age of a fossil by measuring carbon isotope ratios and applying the known decay laws.
**Input Box:**
[Enter the calculated age of the fossil in years, rounded to one decimal place.]
**yrs**
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