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Calculating ln in radioactive decay

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data

    Radioactive decay is:

    N = N0e-λt

    N can also be used to describe count rate after a time, (t) where N0 is intial count rate and λ is decay constant.....

    Half life, t1/2 od radioactive isotope is

    t1/2 = 1n2
    λ

    The λ should be under the ln2 but it won't let me underneath

    How do I calculate 1n??

    For example if time (t) in minutes is 10 and Count rate in 1 minute (N) is 82 what is 1n

    I dont understand at all? Any helps is grealty appreciated

    Thanks

    2. Relevant equations

    As above

    3. The attempt at a solution

    I found ln on the calculator but confused how I get the answer from t as and n......

    I am doing as biology degree but doing a physics module which I am struggling with
     
  2. jcsd
  3. Feb 10, 2013 #2

    tms

    User Avatar

    The equation for decay is
    [tex]N = N_0 \,e^{-\lambda t}.[/tex]
    To find the half-life, set [itex]N = N_0/2[/itex]:
    [tex]
    \begin{align}
    \frac{N_0}{2} &= N_0 \,e^{-\lambda t} \\
    \frac{1}{2} &= e^{-\lambda t}.
    \end{align}[/tex]
    Now you just solve for [itex]t[/itex]:
    [tex]
    \begin{align}
    \ln \frac{1}{2} &= -\lambda t \\
    t &= - \frac{1}{\lambda} \ln \frac{1}{2}.
    \end{align}[/tex]
     
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