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Radioactive Decay

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    A radioactive sample contains 3.25 1018 atoms of a nuclide that decays at a rate of 3.4 1013 disintegrations per 26 min.
    (a) What percentage of the nuclide will have decayed after 159 d?

    (b) How many atoms of the nuclide will remain in the sample?

    (c) What is the half-life of the nuclide?

    2. Relevant equations

    The equations I used were
    t1/2 = ln2/k to find the half life
    and N'=Ne-kt

    3. The attempt at a solution

    I used the equations above and solved for part b, the number of atoms and found this to be 2.976E18 --which IS correct. I converted the 159 days into minutes, and found k by taking the rate (now in days) and dividing by the original number (N) and getting 3.836E-7 for k

    I then plugged this into N*e-kt with t now in minutes and got my answer for part B. (2.976E18 atoms).

    So my problem is with part 1 and 3....I thought it would be pretty straight forward, subtracting hte remaining atoms from the original to get the amount that decayed. Then taking that amount, dividing it by the original to get hte percent decayed. I keep getting 8.43% for this....but it's incorrect.

    Finally for C, I thought I would just convert everything back to days, then take ln2/k (in days now) to get the half life...but I guess something is wrong here too. Can someone please explain how to do this? Thanks!
  2. jcsd
  3. Apr 16, 2010 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Your methods are correct. You could be making errors in arithmetic. For what it's worth, I get 8.46% for part (a).
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