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Homework Help: Calculating radioactivity after a period of time

  1. May 31, 2013 #1
    1. The problem statement, all variables and given/known data

    A cancer patient is typically given an intravenous dose of Metastron with an activity of
    148 MBq.
    Calculate the activity after 6 months (183 days).

    Physical half-life of Metastron = 50.5 days
    Biological half-life of Metastron = 1.8x104 days

    2. Relevant equations

    T1/2 = [itex]\frac{ln2}{λ}[/itex]

    [itex]\frac{ΔN}{Δt}[/itex] = λN

    N = N0e-λt

    3. The attempt at a solution

    The equation used to calculate the activity would be
    N = N0e-λt

    N0 = 148MBq
    t = 183days

    So I just need to find λ. - This is where I think I am going wrong.

    λ = [itex]\frac{ln2}{T}[/itex]
    λ = [itex]\frac{0.693}{50.5days}[/itex]
    λ = 1.59x10-7

    Substituting this into the first equation gets...

    N = N0e-λt
    N = 148 e-(1.59x10-7) x 183
    N = 147.996MBq
    N = 148MBq

    The correct answer is (apparently) 11.95MBq.
    Seeing as all values are in MBq and days, I don't think I have to convert to Bq and seconds (actually even if I do convert I still get an incorrect answer).
    Therefore I think I am stuffing up at my calculation of λ. But I don't see any other way in which I can calculate it. Am I correct in thinking this is where I am going wrong?
  2. jcsd
  3. May 31, 2013 #2
    1. You are pressing the wrong buttons on your calculator: ## \frac{ln2}{50.5} \approx 0.013726 ## which would give an answer of 12.01MBq.
    2. You are ignoring the biological half life; treating this correctly gives an answer of 11.92MBq if 6 months is taken as 183 days, or 12.00MBq after 365/2 = 182.5 days.
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