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Half-life Stuff

  1. Feb 22, 2006 #1
    Something has a half-life of 18.4 days. How much time will a 50-mg sample take to decompose to 10 mg?
    My steps
    50(1/2)^n/18.4 = 10(1/2)^n/18.4
    25^n/18.4 = 5^n/18.4
    (5^2)^n/18.4 = 5^n/18.4
    5^2n/18.4 = 5^n/18.4
    Exponent view
    2n/18.4 = n/18.4
    2n-n = 18.4/18.4
    n=1
    Am i doing something wrong?
     
  2. jcsd
  3. Feb 22, 2006 #2
    half life equation is
    [tex] q(t) = q_{0} 2^{-t/\tau} [/tex]
    where q(t) is the quantity after time t,
    q0 is the initial quantity
    tau is the half life

    do u see your mistake?
     
  4. Feb 23, 2006 #3
    Y=CoE^kt
    Co = initial amount
    Y= what amount is left
    K= rate
    T= time
    First you have to find the rate
    Since in 18.4 days you will have 1/2 left you set it up like this:

    1/2Co=CoE^kt
    Now the Co's cancel and you're left with :
    1/2=e^kt
    t=18.4
    1/2=e^k(18.4)
    Take the natural log of both sides now
    ln(.5)=lne x 18.4k
    -.6931471806 = 1 x 18.4k
    divide by 18.4
    k = -.0377
    Now you must find the time it takes to go from 50 to 10.
    10=50e^kt
    k we know = -.0377 and we're looking for t

    You should be able to figure it out from here.


    (sorry if my work doesn't look fancy, I'm new to this stuff - I'll pick it up eventually)
     
  5. Feb 23, 2006 #4

    HallsofIvy

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    Science Advisor

    This: 50(1/2)^n/18.4 = 10(1/2)^n/18.4 is your error.
    You want to end with 10 g so you want
    50(1/2)^(n/18.4)= 10
     
  6. Feb 23, 2006 #5
    Thank you HallsOfIvy for being specific for me:)
     
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