Question

Let αdt be the probability of a gas molecule experiencing a collision during the time interval dt; α is a constant. Find:

(a) the probability of a molecule experiencing no collisions during the time interval t;

(b) the mean time interval between successive collisions.

Answer 1

(a) Let P (t) = probability of no collision in the interval (0, t). Then 

where we have used P (0) = 1 

(b) The mean interval between collision is also the mean interval of no collision. Then