How Do You Calculate the Age of Plant Material Using Radioactive Decay?

AI Thread Summary
To calculate the age of plant material using radioactive decay, the decay constant for 14C is determined to be 3.9 x 10-12 s. The problem involves understanding the ratio of 12C to 14C after the plant's death, as 14C decays over time. The number of carbon atoms in 1 gram of carbon can be calculated using the concept of moles, where 1 mole of carbon equals approximately 6.022 x 10^23 atoms. The decay rate of 3 disintegrations per minute per gram of carbon provides the necessary data to find the number of 14C atoms and their mass. This approach allows for the estimation of the plant's age based on the remaining 14C.
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Homework Statement


This problem involves calculating the age of plant material from which 3 radioactive disintergrations per minute per gram of carbon are detected. During its lifetime, the plant took in carbon from the atmosphere. Of this carbon, for every 1012 atoms of normal 14C, there was 1 atom of radioactive 14C. When the plant died, the 14C decayed so the proportion of 12C to 14C increased.

The half life of 14C is 5570 years. The mass of a 12C is 1.993 x 10-23kg.

How many carbon atoms (12C and 14C) arein 1 gram of carbon?


Homework Equations


t (time in seconds) = ln2/λ

( λ is decay constant)

n = n0 exp (- λt)

n0 is the number of nuclei present at time


The Attempt at a Solution


I'm sorry, I know the question seems well explained, but I'm still confused on how to solve it. I've worked out that the decay constant of 14C is 3.9 x 10-12s.
After that I'm not sure what to do to find out how many atoms there are in 1g of carbon... I'msorry fornot attempting much, but I'm so confused. Please may I have some guidance on what to do? Thank you.
 
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If there is 1 mole of atoms in 12 grams of carbon, how many atoms are in 1 gram?
 
daveb said:
If there is 1 mole of atoms in 12 grams of carbon, how many atoms are in 1 gram?

1/12..or 0.083mols?
Ah, thank you, I didn't know we had to use moles.
 
You don't have to use moles. You are given the number of decays per second; in other words, you are given dn/dt. You can then calculate the number of C14 atoms, and then their mass. The rest of the 1 g are C12.
 
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