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Homework Help: Radioative Decay

  1. Dec 19, 2009 #1
    1. The problem statement, all variables and given/known data
    dN/dt, is proprotional to the number of nuclei present, N.

    How would you linearize data that you collected?

    2. Relevant equations



    3. The attempt at a solution
    I'm confused about what the data would look like. Would I be given something like N = 4, or N=4t?

    To graph it so it comes out as a straight line, would I take the derivative of N and plot that against dN/dt? Or do I plot N vs t?
     
    Last edited: Dec 19, 2009
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  3. Dec 19, 2009 #2

    Astronuc

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    Write the first order differential equation according to the information given. One is given, dN(t)/dt, N(t) and constant of proportionality, λ. Note that N(t) is decreasing.


    With each half-life, the number of atoms is approximately equal the number of atoms at the beginning of the half-life period.
     
  4. Dec 19, 2009 #3

    Andrew Mason

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    The solution to this differential equation:

    [tex]\dfrac{dN}{dt} = \lambda N[/tex]

    is the function:

    [tex]N = N_0e^{\lambda t}[/tex]

    So plot the data for N(t) on the y axis and time, t, on the x axis, and take the slope at different points. Then plot the data for N(t) (y axis) vs. the slope of this first graph (x axis) on another graph. What kind of a graph is the second graph? How do you determine [itex]\lambda[/itex] from the second graph?

    AM
     
  5. Dec 19, 2009 #4
    The second graph would be linear, and λ is the slope?

    Just wondering, could I also do it this way? If I solve the differential equation to get ln(N) - ln(No) = -λt, and graph t vs ln(N)?
     
  6. Dec 19, 2009 #5
    Also, how do you get the equation -dN/dt = λN into the form ln(N) - ln(No) = -λt?

    I know I need to solve the differential equation but I'm getting -ln(N) = -λt. Where does the ln(No) come from and why is ln(N) positive?

    EDIT: nevermind, I figured it out =)
     
    Last edited: Dec 19, 2009
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