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Radioactive decay question

  1. Apr 6, 2012 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations
    t (time in seconds) = ln2/λ

    ( λ is decay constant)

    n = n0 exp (- λt)

    n0 is the number of nuclei present at time


    3. 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.
     
  2. jcsd
  3. Apr 6, 2012 #2
    If there is 1 mole of atoms in 12 grams of carbon, how many atoms are in 1 gram?
     
  4. Apr 6, 2012 #3
    1/12..or 0.083mols?
    Ah, thank you, I didn't know we had to use moles.
     
  5. Apr 6, 2012 #4

    tms

    User Avatar

    You don't have to use moles. You are given the number of decays per second; in other words, you are given [itex]dn/dt[/itex]. 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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