How do I determine the age of a sample using radiocarbon dating?

  • Thread starter mss90
  • Start date
In summary, the conversation is discussing how to determine the age of a sample of carbon with a mass of 9.2g and an activity of 1.6Bq. The questioner is unsure how to solve this without knowing the isotope and halflife of carbon, but the responder suggests using carbon-14 dating and provides equations to find the initial amount of carbon-14 and the time passed since it was formed. The conversation also mentions the use of Avogadro's number to convert from atoms to moles.
  • #1
mss90
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Homework Statement


9.2g of carbon got an activity of 1.6Bq, how old is it?

Homework Equations


A = -(lambda)*N
N=No * e ^ -(lambda)*t
(lambda) = ln2/t1/2

The Attempt at a Solution


The question doesn't specify which isotope of carbon it is so halflife remains unknown.
I can't see how to solve this by only knowing the mass and activity.
Could anyone give me pointers?

R
 
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  • #2
They are most likely referring to carbon-14 dating.
 
  • #3
Alright in that case we know the half life and can find the decay constant.
Using A = -(lambda)*N we can find N as well (not sure If I need to divide the activity on 9.2g to get it per grams?)
However It still leaves No and t unsolved.

An alternative method is to; N=No * e ^ -(lambda)*t |*(lambda) => A=Ao * e ^ -(lambda)*t
But it seems to get me to the same "deadend" where Ao and t is unsolved.
I thought I might be able to set t=0 to get Ao but that only makes the expression " e ^ -(lambda)*t" equal 1.
Any tips?

R

PS: thanks for fast reply
 
  • #4
Atoms per mole.
The sample starts out with a certain fraction of it being carbon-14.
Over time the amount of carbon-14 decays.
 

Related to How do I determine the age of a sample using radiocarbon dating?

What is radiocarbon dating?

Radiocarbon dating is a method used by scientists to determine the age of organic materials. It measures the amount of carbon-14, a radioactive isotope of carbon, in a sample and compares it to known levels to estimate the age of the sample.

How accurate is radiocarbon dating?

Radiocarbon dating is generally considered accurate within a range of 100-200 years. However, the accuracy can vary depending on the sample and the laboratory conducting the dating. It is important to note that radiocarbon dating can only provide an estimate of age, not an exact date.

What types of materials can be dated using radiocarbon dating?

Radiocarbon dating is primarily used on organic materials, such as bones, plants, and wood. It is not typically used on inorganic materials, such as rocks or minerals, as they do not contain carbon.

What are the limitations of radiocarbon dating?

Radiocarbon dating is limited to materials that were once living and have not been contaminated by external sources of carbon. It also has a maximum age limit of approximately 50,000 years, as the amount of carbon-14 in a sample becomes too small to accurately measure beyond this point.

How is radiocarbon dating used in other fields of science?

Radiocarbon dating is not only used in archaeology and anthropology, but also in other fields such as geology, paleontology, and environmental science. It can be used to date geological events, such as volcanic eruptions, and to track changes in the Earth's climate over time.

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