- #1

derravaragh

- 24

- 0

## Homework Statement

Molecules in an ideal gas collide with each other at random times. The probability distribution governing the time between collisions is P(t) = Ae^(-bt).

(a) Find the value of A so that P(t) is correctly normalized.

(b) Find the average time between collisions, t. This time is traditionally called tau. Now re-write P(t) in terms of tau, without the original parameters A and b.

(c) Find the standard deviation of the collision times, σ_t.

## Homework Equations

∫(x^n)e^(-x/a)dx = n!a^(n+1) from 0 to ∞

## The Attempt at a Solution

I believe I have the right answer to (a), I normalized it to obtain P(t) = -be^(-bt), but I can't figure out what to do for part (b) on.

My attempt was to take the average time t to equal (ƩP(t))/n where n is the number of collisions and the sum goes from 0 to ∞, but that thought process got me no where. Any help would be appreciated.