Question

The collision diameter for helium is 207 pm and for methane, 414 pm what is the ratio of mean free path of He compare to that
with methane under the same conditions?

Answer 1

Answer:

2R

Figure 1: Cross Section.

Chapter 3

3.8 Mean Free Path and Diffusion

In a gas, the molecules collide with one another. Momentum and energy are conserved

in these collisions, so the ideal gas law remains valid.

The mean free path λ is the average distance a particle travels between collisions.

The larger the particles or the denser the gas, the more frequent the collisions are and

the shorter the mean free path. If the particle were all by itself, then the mean free path

would be infinite. If 2 particles, each of radius R, come within 2R of each other, then

they collide. The collision cross section is defined as the collision area σ = π(2R)

2

that

it presents as it moves through space.

The mean free path λ is related to the cross section σ and the number density n of

particles by

λ ≈

1

nσ

(1)

To see this, notice that a particle that undergoes a large number N of collisions will

exhibit a zig-zag pattern of total length L = Nλ, since the average distance between

collisions is λ. We can think of the particle as sweeping out a volume

V = Lσ = Nλσ (2)

The number density of particles in this volume is n:

n =

N

V

=

N

Nλσ =

1

λσ (3)

where we are assuming that the number of collisions in the volume is the same as the

number of molecules in the volume, and that the number density in the volume is the