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Decay Rate

  1. May 31, 2015 #1
    1. The problem statement, all variables and given/known data
    An initially pure 3.4 g sample of Ga-67, an isotope with a half life of 78 hr.
    What is its initial decay rate?

    Note: Molar Mass values given in tables for chemical elements are for natural mix isotopic ratios. (i.e. the relative percentages of each isotope normally present in natural samples). The Molar Mass (in g/mol) for a pure isotope is equal to its atomic mass (in amu). (Answer in Bq, correct to 3 significant figures)

    Avogadro's Number = 6.022045*1023 g/mol
    Ga-67 = 66.9282049 u = 66.9282049 g/mol
    Half-life = T1/2 = 78 Hr

    2. Relevant equations
    N = [ Avogadro's Number / 66.9282049 g/mol ] * 3.4 g
    λ = ln(2) / T1/2
    Decay Rate = -λ*N

    3. The attempt at a solution
    N = [ 6.022045*1023 g/mol / 66.9282049 g/mol ] * 3.4 g
    = 3.059241321 * 1022

    λ = ln(2) / 280800
    = 0.00000246847

    Decay Rate = 0.00000246847 * 3.059241321 * 1022
    = 7.5516454*1016 Bq
    = 7.55*1016 Bq (Correct to 3 sig figs)

    This doesn't seem correct. I've got the atomic mass and therefore the molar mass of Ga-67, but to calculate N (nuclei) should I have subtracted the electrons from the atomic mass / molar mass?
     
  2. jcsd
  3. May 31, 2015 #2

    mfb

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    Staff: Mentor

    While this is right, you are supposed to take another value: "The Molar Mass (in g/mol) for a pure isotope is equal to its atomic mass (in amu)"
    The difference is large enough to influence the final result with 3 significant figures.

    The electrons are fine, they are still part of the sample so there is nothing to subtract.
     
  4. May 31, 2015 #3
    What other value should I use for the molar mass of Ga-67? Is there a way of converting the atomic mass I have to the correct molar mass to use in this question?
     
  5. May 31, 2015 #4

    mfb

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    Staff: Mentor

    A sorry I misread the quoted part, somehow I thought the problem statement suggested to use 67 u as mass (not so uncommon in problems to neglect the difference between A and mass in u).
    If this is an online test without limited attempts, you can try that.

    I get the same answer as you so I don't know where the problem is.
     
  6. May 31, 2015 #5
    1 attempt only I'm afraid!

    Decay Rate = -λ*N

    so should it be = - 7.55*1016 Bq?
     
  7. May 31, 2015 #6

    mfb

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    Staff: Mentor

    Yes.
     
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