What is probability per unit time

mcodesmart

I am reading Aschroft and Mermin and I came across the probability per unit time

I have trouble understanding the concept as it is. But they do try to explain.

They say that the probability that an electron will experience a collision in an ifinetismal time, dt, is just dt/τ.

From this i gather, that if the time dt is close to 0, the probabitly will be small. If the time dt is equal to τ, then the probability that an electron will collide is 1.

But in the next sentence, they say that τ is an average time that a collision will occur, meaning that the probability that it will occur at time τ cannot be 1, because if it is an average time, then, collision will occur sometimes longer that τ and sometimes shorter that time τ. All this has got me confused and I need some clarification.

tiny-tim

hi mcodesmart!
this is like half-life …

the probability of no collision after time t will be e^-t/τ

mcodesmart

I see.. it is not the probability of collision but the probability of NO collision..

Can you please explain how you get that from the statement that I provided in the OP..

tiny-tim

(just got up )
oh come on …

you do a bit of research and calculation, and see if you can get that equation!