Calculating decay constants and half-life

  1. A scientist wishes to find the age of a sample of rock. Realising that it contains radioactive potassium, which decays to give a stable form of argon, the scientist started by making the following measurments:

    decay rate of the potassium in the sample = 0.16Bq
    mass of potassium in the sample = 0.6x10^-6g
    mass of argon in the sample = 4.2x10^-6g

    The Molar mass of the potassium is 40g. show that the decay constant for potassium is 1.8x10-17 and its half-life is 1.2x10^9years.



    2. Relevant equations

    decay constant = a/N
    n=m/Mr

    3. The attempt at a solution


    N=m/Mr
    N=0.6x10^-6/40
    N=1.5x10^-8

    N=1.5x10^-8 x 6.02x10^-8
    N=9.03 x 10^-16

    decay constant = a/N
    decay constant = 0.16/9.03x10^-16

    I got this far then got stck as the answer was wrong, im not sure wher to go from here any help would be appreciated.
     
  2. jcsd
  3. Hootenanny

    Hootenanny 9,677
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    You might want to check the value of Avogadro's Constant :wink:
     
  4. oops that should have been 10^23 lol, thanks i'll try that
    x
     
  5. now i get 1.4448x10^15 which is still wrong, im so confused.
    x
     
  6. Hootenanny

    Hootenanny 9,677
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    Your method is correct, you must just be punching the numbers into your calculator wrong. How many K atoms did you calculate?
     
  7. 9.03x10^15
    x
     
  8. Hootenanny

    Hootenanny 9,677
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    Looks right to me.
     
  9. well i dont know what i did but i have just gotten the right answer thanks lol
    xx
     
  10. Hootenanny

    Hootenanny 9,677
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    As I said above, your method was spot on but you were probably just hitting the wrong buttons on your calculator.
     
  11. thanks lol, i do that alot it seems, better brush up on those skills before the exam lol.
     
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