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Trying to set these equations up

  1. Sep 12, 2011 #1
    I've been working on math this morning, and these two equations I can't figure out. I have a test tomorrow and want to understand how to set them up in case theyre on the test.
    Equation 1
    Uranium 235 is used as fuel for some nuclear reactors. It has a half-life of 710 million years. How long will it take 10 grams of uranium 235 to decay to 1 gram? --- answer is 2,360 million years



    Equation 2
    You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 2 days later you determine that it has decayed down to 0.7 grams. What is its half-life? --- answer is 3.89 days


    I've been trying various ways of setting these up with pe^rt and A(.999879)^t and simplifying with logs to no avail. If someone can help me please do!
     
  2. jcsd
  3. Sep 12, 2011 #2

    HallsofIvy

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    Where did you get ".999879"? The one thing that is directly given in each problem is "A".
     
  4. Sep 12, 2011 #3
    It's a general equation that the book gives. The entire thing reads C(t) = A(0.999879)^t
     
  5. Sep 12, 2011 #4
    The general form of the equation would be N(t) = N(0)e-t*ln2/T, where T is the half-life, and N(0) is the number of atoms at time t = 0. So for each one, you have all the information you need.
     
  6. Sep 12, 2011 #5
    How would you set it up though?? I know I have all the information I just can't figure out where to put the information. For the first equation if I put 0 in for t the equation doesnt work out...if I put e-(10)*ln2/710 that doesnt work either.
     
    Last edited: Sep 12, 2011
  7. Sep 12, 2011 #6
    After a lot of hard work, I finally managed to figure out equation one.

    I realize now daveb gave me the equation, but I didn't understand it.

    So the equation would read: 1/10 = e^-([ln2]/710)t => ln(1/10) = -([ln2]/710)t => t = ln(1/10)/-([ln2]/710) = 2,360



    I still am trying to figure out equation 2 but am confused
     
  8. Sep 12, 2011 #7

    eumyang

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    Use the equation that daveb gave again:
    N(t) = N(0)e-t*ln2/T

    You're given that if t = 2, N(t) = 0.7. Solve for T. (While he said that N(0) = number of atoms at t = 0, it doesn't have to be in terms of atoms. It could be in terms of moles, or grams.)
     
  9. Sep 13, 2011 #8
    THANK YOU! I never even thought of setting it up like that. I just get confused because theres so many equations, and it isn't explained thoroughly enough in class, as well as the examples the book gives aren't very helpful.
     
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