1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating radioactivity after a period of time

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

    QUESTION
    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).

    PREVIOUS INFORMATION
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculating radioactivity after a period of time
Loading...