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Half Life - Calculate Fraction Remaining

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Carbon 14 has a half-life of 5730 years, what fraction will have decayed in 2300 years?

    2. Relevant equations


    Nf/No =e^-kt

    3. The attempt at a solution

    Nf/No =e^-1.21 x 10^-4 x 2300

    =0.068585374

    However if I use Nf =No(1/2)^2300/5730

    I get 0.757125224

    I appreciate that i'm looking for the fraction that has decayed but i'm unsure as to why this has produced 2 different answers, I thought either could be used for this problem.

    Thanks
     
  2. jcsd
  3. Mar 4, 2012 #2

    Doc Al

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    Staff: Mentor

    Redo this.
     
  4. Mar 4, 2012 #3

    gneill

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    Staff: Mentor

    Recheck your math for the first formula.

    EDIT: Doc Al beat me to it again.
     
  5. Mar 4, 2012 #4

    BruceW

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    Homework Helper

    I agree with them guys. You got it right using the second method jendrix. But maybe just a mistake while calculating using the first method.
     
  6. Mar 4, 2012 #5
    Hi, I think I was using a wrong value for the decay constant but somehow wrote it down correct here.

    My new answer is 0.77130147

    I was wondering why there is a discrepancy albeit a small one depending on which formula I use, is it to do with the rounding of the constant?
     
  7. Mar 4, 2012 #6

    Doc Al

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    Staff: Mentor

    You're still making an error somewhere. Just evaluate the formula you gave in your first post:
    That should give you the right answer.
     
  8. Mar 4, 2012 #7
    Thanks Doc Al, I now get 0.757069666 as opposed to 0.757125224 from the other formula.
    Is this where rounding the constant has had an effect?

    Now I have to find the fraction that was lost to decay, if i do 1 - 0.757069666 to give 0.242930334 would you consider this sufficient or should I call it 6/25?
     
  9. Mar 4, 2012 #8

    Doc Al

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    Staff: Mentor

    Yes. (But round off your answers to a reasonable number of significant figures.)
    That decimal should be fine (rounded off, of course). (When they say 'fraction' they probably don't literally mean fraction, as in numerator/denominator.)
     
  10. Mar 4, 2012 #9
    Excellent, thanks for all your help guys :smile:
     
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