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Need help on a half life equation

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Given Y=Ae-t/(lambda) find the half life in terms of A and lambda


    2. Relevant equations

    Y=Ae-t/(lambda)

    3. The attempt at a solution
    every time t is a multiple of lambda the relationship then becomes (lambda(n)=A/e^n), i cant figure out how that will relate, i also tried setting the equation to A/2 however that just canceled out the A. Need help!
    I figured it out t(1/2)=ln(2)/lambda, however i dont know how to incorporate A into this
     
    Last edited: Sep 10, 2009
  2. jcsd
  3. Sep 10, 2009 #2

    rl.bhat

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    Homework Helper

    Expression of radioactive is written as
    A = Ao*e^-λt.......(1)
    As you have mentioned
    t_1/2 = ln(2)/λ.
    The equation (1) can be written as
    A/Ao = e^-λt. or
    Ao/A = e^λt
    Take logarithm of both the side and fine the expression for λ. Put it in the t_1/2 equation.
     
  4. Sep 10, 2009 #3
    rl.bhat if i put the expression into lambda in the t_1/2 equation then i lose the lambda, i need to express it in lambda and A
     
  5. Sep 10, 2009 #4

    rl.bhat

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    In that case
    t_1/2 = ln(A/Ao)/λ
     
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