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!

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
  2. jcsd
  3. Dec 19, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Science Advisor
    Homework Helper

    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?

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