How Do You Calculate Radioactive Dating Errors?

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SUMMARY

This discussion focuses on calculating radioactive dating errors, specifically using uranium-238 and lead-204 ratios to date igneous rock samples. The user incorrectly calculated the fraction of original uranium remaining in a rock sample containing three times as many lead atoms, arriving at 1/3 instead of the correct answer of 1/4. Additionally, the user miscalculated the age of the rock based on the half-life of uranium-238, stating 6200 million years instead of the correct 9000 million years. The discussion also touches on carbon-14 dating of historical artifacts, such as a linen shirt believed to belong to St. Thomas Becket.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with uranium-238 and lead-204 isotopes
  • Basic knowledge of carbon-14 dating techniques
  • Ability to perform ratio and proportion calculations
NEXT STEPS
  • Study the principles of radioactive decay and half-life calculations
  • Learn about the uranium-lead dating method and its applications
  • Research carbon-14 dating and its limitations in archaeological contexts
  • Explore common mistakes in radioactive dating calculations and how to avoid them
USEFUL FOR

Students in geology, archaeology, and anyone interested in understanding the principles of radioactive dating and its applications in determining the age of rocks and artifacts.

reree17
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These are just a few practice questions I found difficult, I would appreciate it if you could provide step-by-step explanation on how to solve the following problems. I checked all my answers in the textbook and got the following wrong, but cannot work out how to arrive at the right answer. Thank you so so so much in advance!

1) The relative proportions of uranium-238 and lead-204 in a sample of igneous rock can be used to date the rock. A rock sample contains three times as many lead atoms as uranium atoms.
(I) What fraction of the original uranium was left in the rock? Assume that there was no lead in the original rock - My answer was 1/3 but the answer in the book was 1/4. How?
(ii) the half-life of uranium-238 is 4500 million years. Calculate the age of the rock.- I got 6200 million for this but the book says 9000 million years, I do not understand how this answer was arrived at.

6a) Linen is a cloth made from the flax plant. A recent exhibition included part of a linen shirt, believed to have belonged to St. Thomas a becket, who died in 1162. Extracting carbon-14 from the cloth would allow the age of the shirt to be verified. If 1g of carbon-14 extracted from the cloth were to give 870 counts in 1 hour, would it be possible to have once belonged to St thomas a becket? Clearly show the steps and the reason for your decision. - I did 1 x 1162 = 870/2 = 435 but then got confused after that.
 
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hi reree17! :smile:
reree17 said:
) The relative proportions of uranium-238 and lead-204 in a sample of igneous rock can be used to date the rock. A rock sample contains three times as many lead atoms as uranium atoms.
(I) What fraction of the original uranium was left in the rock? Assume that there was no lead in the original rock - My answer was 1/3 but the answer in the book was 1/4. How?

if there were originally 12 atoms of uranium, then … ? :wink:
 

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