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

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AI Thread Summary
To determine the age of a carbon sample using radiocarbon dating, the decay constant and half-life of carbon-14 are essential, as the activity and mass alone are insufficient for calculation. The user struggles with the equations due to the unknown initial amount of carbon-14 (No) and the half-life not being specified. They explore using the formula A = -(lambda)*N but find themselves at an impasse regarding the values of Ao and t. An alternative approach using N=No * e^-(lambda)*t also leads to unresolved variables. Understanding that the sample's initial carbon-14 fraction decreases over time is crucial for accurate age determination.
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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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They are most likely referring to carbon-14 dating.
 
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
 
Atoms per mole.
The sample starts out with a certain fraction of it being carbon-14.
Over time the amount of carbon-14 decays.
 
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