How Do You Calculate Radioactive Dating Errors?

AI Thread Summary
The discussion focuses on calculating radioactive dating errors, specifically using uranium-238 and lead-204 ratios to date igneous rock. A participant struggles with determining the fraction of original uranium remaining, believing it to be 1/3, while the textbook states it is 1/4. They also miscalculate the age of the rock, arriving at 6200 million years instead of the correct 9000 million years based on uranium-238's half-life. Additionally, there is a question regarding the dating of a linen shirt believed to belong to St. Thomas Becket, with confusion arising from the calculations related to carbon-14 counts. Clarifying these calculations is essential for accurate radioactive dating.
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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