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Radio Actice Decay

  1. Jul 17, 2003 #1
    Libby's observation that all the carbon in the world's living cycle is kept uniformly radioactive through the production of C-14 by cosmic radiation led to his development of the radioactive carbon dating method. Samples of carbon in the life cycle have been found to have a disintegration rate of 15.0 disintegrations per gram per minute. Upon death of the living organism, the life cycle ceases and the C-14 in the material decays with a half-life of 5730 years. If an archaeological sample was determined to have a disintegration rate of 0.03 disintegrations per gram per minute, how old is the sample?

    This problem is killing me.

    So far the real thing I've been able to find is how long the sample has been dead:

    t = ln(2 &lambda No)/lambda

    No = the initial number of radioactive nuclei

    Can I get a hint?
  2. jcsd
  3. Jul 17, 2003 #2
    Well, you know that the total C-14 content decreases by a factor 1/2 during one half-life. This is of course also true for the disintegration rate. Now, you know that the disintegration rate has gone down from 15.0 to 0.03. How many half-lifes did that take?
  4. Jul 17, 2003 #3
    That's an interesting way to look at the problem.

    I'll see what I can do with that.

  5. Jul 17, 2003 #4
    I get:

    t = 1.62 x 1012s

    Is this correct?



    Which is 51374 years.

    I just looked up how old C-14 dating is good too. It said 50,000 years. So it looks like I'm right.

    This problem was easy, I don't know why I struggled with it so much!
    Last edited: Jul 17, 2003
  6. Jul 18, 2003 #5
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