Calculating Age of Old Sample with Carbon 14 Dating

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In summary, the problem asks for the age of an old sample of vegetation based on the amount of 14C present. The relevant equation for this problem is ln(N/Nsub0)=-.693t/tsub(1/2), where N represents the amount of radioactive material remaining after time t, No is the original amount of radioactive material, and T is the half life. A possible approach to solving this problem is to use the equation N=No*(1/2)^t/T.
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Sublime74
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Homework Statement



The amount of 14C in an old, isolated sample of vegetation is 0.692 that expected from a present day sample with an equivalent carbon content. Calculate the age of the old sample in years.


Homework Equations



Im fairly sure you use the following equation to solve this...ln(N/Nsub0)=-.693t/tsub(1/2) ...I could be wrong, because every time I attempt to use it nothing happens haha.

The Attempt at a Solution

 
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Try N=No*(1/2)^t/T

No = original amount of radioactive material
N = amount of amount of radioactive material remaining after t
t = time intercal
T =half life
 
  • #3


I can confirm that the equation you have provided is indeed the correct one to use for calculating the age of an old sample using carbon-14 dating. However, it is important to make sure that all units are consistent and to use the correct value for the half-life of carbon-14, which is approximately 5,730 years.

Using the given information, we can rewrite the equation as ln(0.692) = -0.693t/5730. Solving for t, we get t = (-5730 ln(0.692))/-0.693 = 17,670 years. Therefore, the age of the old sample is approximately 17,670 years.

It is also important to note that carbon-14 dating can only provide an estimate of the age of a sample, as there are many factors that can affect the accuracy of the results. These factors include the variations in the amount of carbon-14 in the atmosphere over time and the possibility of contamination. Therefore, it is important to use multiple dating methods and to interpret the results carefully.
 

Related to Calculating Age of Old Sample with Carbon 14 Dating

1. How does carbon 14 dating work?

Carbon 14 dating is based on the principle that all living organisms contain a small amount of radioactive carbon in their cells. When an organism dies, it stops absorbing carbon and the amount of radioactive carbon begins to decrease. By measuring the ratio of radioactive carbon to stable carbon in a sample, scientists can determine how long ago the organism died.

2. What is the half-life of carbon 14?

The half-life of carbon 14 is approximately 5,730 years. This means that after 5,730 years, half of the initial amount of radioactive carbon in a sample will have decayed into stable carbon. After another 5,730 years, half of the remaining radioactive carbon will have decayed, and so on.

3. How accurate is carbon 14 dating?

Carbon 14 dating is a highly accurate method for determining the age of organic materials up to about 50,000 years old. However, it may be less accurate for samples that are more than 50,000 years old because the amount of radioactive carbon in the sample is too small to be accurately measured.

4. Can carbon 14 dating be used for non-organic materials?

No, carbon 14 dating can only be used for organic materials such as plants, animals, and humans. This is because these organisms absorb carbon from their environment, whereas non-organic materials do not.

5. How can we be sure that the carbon 14 dating results are accurate?

Scientists use multiple methods to ensure the accuracy of carbon 14 dating results. This includes calibrating the results with other dating methods, such as tree rings or ice core layers, and using multiple samples from the same site to confirm consistency. Additionally, scientists continuously refine and improve the techniques used in carbon 14 dating to increase accuracy.

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