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Homework Help: Decay of Particle

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data
    We know that the probability of a particle decaying between time t=o and t=t is given by P(t)=e-[tex]\Gamma[/tex]t
    a) Show the probability it decays in time between 0 and [tex]\infty[/tex] is 1
    b) By considering decays at all possible times, calculate the average lifetime [tex]\tau[/tex] of the particle.

    2. Relevant equations
    As above


    3. The attempt at a solution
    Started just by saying that rate of decay = -[tex]\Gamma[/tex]e-[tex]\Gamma[/tex]t but really nothing seems to be getting me to a decay of 1. Any hints would be muchly appreciated.
    Edit: Ok, for the first part, I've argued it by saying that at a time t=0 the proability is 1 that the particle exists, while at a time t=[tex]\infty[/tex] the probability is 0 and so the change in probability is 1. Is that about right? Still can't get started with the second.
     
    Last edited: Feb 7, 2010
  2. jcsd
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