Now we are in a position to calculate the average distance travelled by a group of N0 molecules before they make their first collision. This average distance is known as mean free path l. To calculate the same we multiply x by the number of particles ΔN that travels the distance x before colliding, sum over all values of x, and divide by the total number N0. Thus mean free path is
|
(4.52) |
Following are the features of mean free path:
- Mean free path is inversely proportional to the macroscopic collision cross section.
- Since the unit of macroscopic collision cross section is the reciprocal of the unit of length, the unit of mean free path is the unit of length.
- Mean free path does not depend upon the molecular speed.
- Mean free path increases as pressure is decreased.
Since all the quantities N0, N and x can be measured experimentally,
Eq. (4.50) can be solved for macroscopic collision cross section (nσ)
or mean free path (l).
In terms of mean free path, the survival equation (Eq 4.50) can be written
as
N = N0exp(-nσx) = N0exp(-x/l) |
(4.53) |
Figure 4.10 represents the graphical representation of this equation in
terms of dimensionless ratio 
as a function of
.
Fig. 4.10 Survival Equation (N/N0 versus x/l)
Collision Frequency (z)
Collision frequency is the average number of collisions per unit time made
by a molecule with other molecules. A molecule travels an average distance
of 
in a time interval of Δt in a zigzag
path. The average number of collisions it makes in this time is /l
and hence the collision frequency is
|
(4.54) |
Mean Free time (
)
Mean free time is the average time between collisions and it is reciprocal
to the collision frequency z. Thus
|
(4.55) |
