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Half Life

  1. Jul 30, 2012 #1
    1. The problem statement, all variables and given/known data

    After 25 years, 60% of a radioactive material decays. What is the half-life?

    2. Relevant equations

    I used a ratio of 25/.60= x/.50

    3. The attempt at a solution

    I also tried this ratio as 25/.40= x/.50 Im not really sure what equation I should be using but this ratio set up isnt getting me the correct answer
     
  2. jcsd
  3. Jul 30, 2012 #2
    Decay is an exponential dcay. That is:

    N(t) = N(t0)e-k(t-t0)

    where N(t) is the amount at some time t, N(t0) is the amount at time t0, and k is the decay constant.
     
  4. Jul 31, 2012 #3
    Ok so I tried using this equation but I still got the problem wrong. I used these values:
    N(t)= .6 N(t0)=1 t=25 and t0= 0. I then solved the equation for the decay constant and got: k=.020433025. From my book I found an equation that related the half-life and the decay constant. The equation I used was half-life= ln2/k. from this I got 33.9228861414. This is similar to the answer I got from doing the ratios, and was wrong. I only have one more attempt for full credit and I dont know exactly where I went wrong.
     
  5. Jul 31, 2012 #4

    TSny

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    Note that N(t) represents the amount of radioactive substance that still remains at time t. So, if 60% has decayed, what % remains?

    If you think about it, the half-life should be less than 25 years since more than half has decayed at 25 years.
     
  6. Jul 31, 2012 #5

    HallsofIvy

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    Because you are talking about half life, in particular, I would use the formula (equivalent to the "e" formula TSny gives) [itex]X= C(1/2)^{t/T}[/itex] where C is the initial amount and T is the half life. (You can see that if t=0, [itex]C(1/2)^{0/T}= C[/itex] and if t= T, [itex]C(1/2)^{T/T}= C/2[/itex].)

    If 60% has decayed then 40% is left so [itex].4C= C(1/2)^{25/T}[/itex]. The two "C"s will cancel leaving an equation to solve for T.
     
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