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Homework Help: Difficult nuclear physics exercise

  1. Oct 4, 2004 #1
    nuclear physics exercise

    The activity from a mixed radioactive sample is measured at different times and given in a table like this:

    Time (h).....Decays/sec
    -----------------------
    0.0 ................... 7500
    0.5 ................... 4190
    1.5 ................... 3100
    : ....................... :
    : ....................... :
    12.0 .................. 280

    I am now supposed - based on this table - to determine how many different nuclids the sample consists of along with their half-lives. How can I possibly extract that information uniquely from that table (the numbers in the table aren't exactly the right ones, since I can't remember them).

    maybe the table needs some explanation, because of the crappy layout; the left-hand column is the time in hours and the right-hand column gives the corresponding activities (I haven't written the complete table).
     
    Last edited: Oct 4, 2004
  2. jcsd
  3. Oct 4, 2004 #2

    Tide

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    First, I would suggest making a plot of the data to get a feel for it.

    One approach is to do a least squares fit but you'd have to do it several times for varying numbers of isotopes.

    You might also try doing a numerical Laplace transform. I'm not sure if it can be done but ideally you would see a spike for each nuclide.
     
  4. Oct 4, 2004 #3
    Thanks for answering.

    I'm not sure; do you mean I should try to fit the data to functions like this:

    [tex] f_n(t) = A_1e^{\lambda_1 t} + A_2e^{\lambda_1 t} + \ldots + A_ne^{\lambda_n t} [/tex]

    for various [tex]n[/tex] (corresponding to the number of different isotopes) and see which fit is the best. If so, how can I do this?

    I have no idea what LaPlace transformation is, so I don't think this is what we're supposed to do.
     
  5. Oct 4, 2004 #4
    Tiiiiide! ;)
     
  6. Oct 4, 2004 #5

    Tide

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    Yes, that is what I mean with regard to fitting the data.

    Also, if you have no idea what a Laplace transform is then nevermind!
     
  7. Oct 4, 2004 #6
    Weee! I managed to show that n = 2 using Matlabs curve fitting toolbox. Thank you very much for helping me.
     
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