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Derive relationship between radioactive constant and half life

  1. May 3, 2013 #1

    I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant.

    It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2.

    Thanks in advance
    Last edited: May 3, 2013
  2. jcsd
  3. May 3, 2013 #2


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    Staff: Mentor

    From ##A=A_0 e^{-bt}##, just manipulate the exponential: $$A=A_0 e^{-bt}=A_0 2^{\frac{-bt}{\ln(2)}} = A_0 2^{-\frac{t}{t_{1/2}}}$$
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