Decaying Problem and the Age of a Sample.

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SUMMARY

The discussion focuses on calculating the age of an archaeological wood cellulose sample using carbon-14 dating. Given a half-life of 5730 years for carbon-14, the sample contains 21.0 mg of carbon, which translates to approximately 1.76 x 10^23 total carbon atoms. With an efficiency of 88% in the beta counter, 837 counts were recorded over one week, leading to the determination of the decay constant and the initial decay rate. The final calculations yield the time since the specimen's death, providing a comprehensive method for age estimation in carbon dating.

PREREQUISITES
  • Understanding of carbon-14 dating principles
  • Knowledge of decay constants and half-life calculations
  • Familiarity with beta counting techniques and efficiency
  • Basic skills in stoichiometry and atomic calculations
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  • Learn about the mathematical derivation of decay constants for radioactive isotopes
  • Study the principles of beta decay and its applications in radiocarbon dating
  • Explore the use of shielding in radiation detection and its impact on measurement accuracy
  • Investigate the limitations and assumptions of carbon-14 dating in archaeological contexts
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Students in third-level university courses, archaeologists, and researchers involved in radiocarbon dating and age estimation of organic materials.

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Homework Statement




a living speciman in equilibrium with the atmosphere contains one atom of 14C half life of 5730 for every 7.7x10^11 stable carbon atoms. An archaelogical sample of wood cellulose C12H22O11 contains 21.0mg of carbon. when the sample is placed inside a sheilded beta counter with 88 percent efficiency.837 counts are accumulated in one week. We wish to find the age of the rock.
a) what is the number of carbon atoms?
b)find the number of carbon 14 atoms
c)find the decay constant for carbon-14 in inverse seconds
d)find the initial number of decays per week just after the speciman has died
e)find the corrected number of decays per week from the current sample
f)find the time in years since the speciman died




For a third level university course.
 
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