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Exponential Conundrum

  1. Jan 19, 2013 #1
    1. The problem statement, all variables and given/known data

    Positron Emission Tomography (PET) scanners frequently operate us-
    ing the radioactive isotope 18F, which has a half life of about two hours.
    The isotope is incorporated into a drug, half of which is excreted by
    the body every two hours. How long will it take before the quantity of
    radioactive drug in the body halves?
    A 0.5 hours B 1 hour
    C 1.5 hours D 2 hours

    2. Relevant equations
    Radio active decay is given by :
    where λ ≈ 0.347
    N = [itex]N_{0}[/itex] [itex]e^{-\lambda t}[/itex]

    3. The attempt at a solution

    Assuming that the body excretes every two hours and not during that time, then it is impossible for the drug to get half.
    But unfortunately that answer choice is not present.

    Any help is greatly appreciated .
  2. jcsd
  3. Jan 19, 2013 #2


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    Homework Helper

    Assume that the body excretes the drug continuously.

  4. Jan 19, 2013 #3
    then the obvious answer is "B" ; 1 hour .
  5. Jan 19, 2013 #4


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    Science Advisor

    It's not linear. Try writing down the quantity at 'easy' times - 0, 2hrs, 4hrs, etc. What is the function for the concentration here?

    Tip: [strike]N=N02-t[/strike] N=N02-t/T, where T is the half-life, is an easier way to write your half-life formula.
    Last edited: Jan 19, 2013
  6. Jan 19, 2013 #5
    I considered the "excretion" to vary linearly with time but I never assumed the half life to be the same.

    I deduced the answer by using the correct expression of exponential decay of the radioactive sample.

    Am I still wrong ?
  7. Jan 19, 2013 #6


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    Homework Helper

    Your answer is correct.

  8. Jan 19, 2013 #7


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    Science Advisor

    Sorry - fell victim to the algebraic slip now corrected above. The answer is half a half life, not half an hour. You are correct.
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