# Decay of Particle

1. Feb 7, 2010

### tomeatworld

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-$$\Gamma$$t
a) Show the probability it decays in time between 0 and $$\infty$$ is 1
b) By considering decays at all possible times, calculate the average lifetime $$\tau$$ of the particle.

2. Relevant equations
As above

3. The attempt at a solution
Started just by saying that rate of decay = -$$\Gamma$$e-$$\Gamma$$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=$$\infty$$ 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