Calculating Age of Native American Campfire Using Radioactive Decay of CaCO3

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SUMMARY

The discussion focuses on calculating the age of a Native American campfire using the radioactive decay of calcium carbonate (CaCO3). The process involved burning charcoal to produce CO2, which was then reacted with limewater to precipitate CaCO3. The radioactivity of the CaCO3 was measured at 3.2 d/min, leading to the calculation of the decay constant (k) as 1.2 x 10^-22 min^-1 and a half-life of 5.776 x 10^21 min. The challenge lies in determining the initial and final moles of CaCO3 to accurately calculate the elapsed time since the campfire.

PREREQUISITES
  • Understanding of radioactive decay principles
  • Familiarity with chemical reactions involving CO2 and Ca(OH)2
  • Knowledge of half-life calculations
  • Basic skills in mole conversions and Avogadro's number
NEXT STEPS
  • Research the typical fraction of C-14 in natural samples
  • Learn about the use of decay tables for more precise age calculations
  • Study the principles of radiocarbon dating techniques
  • Explore the impact of atmospheric variations on C-14 levels
USEFUL FOR

This discussion is beneficial for archeologists, chemistry students, and researchers involved in radiocarbon dating and environmental science, particularly those interested in the dating of organic materials using radioactive decay methods.

AryaUnderfoot
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Homework Statement


Archeologists removed some charcoal from a Native American
campfire, burned it in O2, and bubbled the CO2 formed into
Ca(OH)2 solution (limewater). The CaCO3 that precipitated was
filtered and dried. If 4.58 g of the CaCO3 had a radioactivity of
3.2 d/min, how long ago was the campfire?

Homework Equations


C + O2 --> CO2
CO2 + Ca(OH)2 --> CaCO3 + H2O

The Attempt at a Solution


Activity = kN
So k = Activity/N = (3.2 atoms/min)/(0.04576 mol * 6.022*10^23 atoms/mol)
= 1.2*10^-22 min^-1
half life = ln2/k
= 5.776*10^21 min

And that's all I know..I don't have the initial and final moles of the CaCO3, so how should I calculate the time that passed?
 
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You can easily calculate total amount of carbon, and I bet your textbook (or lecture notes) states what is the typical fraction of C-14 in natural samples. If not, you will need to look for this information.

Note, that in reality this is not a single number, as the fraction of C-14 in the atmosphere is not constant. There are tables that can be used to find more precise data.
 

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