Please help me with these radioactive dating questions?

In summary, the conversation discusses the use of uranium and lead proportions to date igneous rocks, as well as the possibility of verifying the age of a linen shirt believed to have belonged to St. Thomas a Becket. The first question asks for the fraction of original uranium left in a rock sample, with the provided answer being 1/4, while the asker's answer was 1/3. The second question involves calculating the age of the rock, with the provided answer being 9000 million years and the asker's answer being 6200 million years. Lastly, the conversation mentions extracting carbon-14 from the linen shirt and determining if it could have belonged to St. Thomas a Becket based on the given information.
  • #1
reree17
17
0
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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  • #2
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:
 

1. How does radioactive dating work?

Radioactive dating is a method used to determine the age of rocks and other materials based on the decay rate of radioactive isotopes. This decay rate is constant and can be used to calculate the age of a sample by comparing the amount of radioactive isotope present to the amount of its decay product.

2. What types of materials can be dated using radioactive dating?

Radioactive dating can be used on a variety of materials, including rocks, fossils, and organic materials such as wood or bone. However, not all materials are suitable for this method, as they may not contain a measurable amount of a radioactive isotope.

3. How accurate is radioactive dating?

Radioactive dating can provide very accurate estimates of the age of a sample, with a margin of error of about 1%. However, the accuracy of the dating depends on various factors such as the type of material being dated and the amount of radioactive isotope present.

4. Can radioactive dating be used to determine the exact age of a sample?

Radioactive dating can provide an estimate of the age of a sample, but it cannot determine the exact age. This is because radioactive decay is a random process, and there may be small variations in the decay rate over time. However, with multiple dating methods and careful analysis, a more precise age range can be determined.

5. What are some limitations of radioactive dating?

One limitation of radioactive dating is that it can only be used to date materials that contain a measurable amount of a radioactive isotope. Another limitation is that it can only provide an estimate of the age of a sample as it cannot determine the exact age. Additionally, external factors such as environmental contamination and the presence of other elements can affect the accuracy of the dating results.

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