Drude theory: Probablity of collision of electron per second

[Aniket1]

The Drude theory assumes the probability that an electron makes a collsion in a second with probabilty 1/ζ where ζ is the relaxation time. Since ζ can be any positive number, the probability can get greater than 1.
What does this mean?

 

[mathman]

Caveat: I know nothing about Drude theory. However in general when talking about relaxation time, the probabilities involved usually have an exponential form. It might mean that the probability that the electron does not collide before time t is e^-t/ζ.

 

[Jano L.]

Yes, that seems right. Another way to understand it: imagine the collisions as random process, for which you know only that on average you get 1/τ collisions per unit time. The exponential probability follows, if I remember well.

 

[Jano L.]

For example: if we expect 10 collisions per second, the probability that after one collision the second one will come after time longer than $t$, comes out as

$$
e^{-t/10}
$$

and decays to zero with time (the longer we wait, the more probable we will get collision in next instant).