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

[Keris]

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.

 

[daveb]

If there is 1 mole of atoms in 12 grams of carbon, how many atoms are in 1 gram?

 

[Keris]

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.

 

[tms]

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.