Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at atm and temperature . Take the radius of a nitrogen molecule to be roughly A. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of ).
Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at atm and temperature . Take the radius of a nitrogen molecule to be roughly A. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of ).

Mean free path is given as

Collision frequency is given as

Successive collision time ≅ 500 x (Collision time)

Pressure inside the cylinder containing nitrogen will be,

P =

Temperature inside the cylinder is given as T = 170 C = 290 K

Radius of a nitrogen molecule is given as r = 1.0 Å = 1 x 1010 m

Diameter will be

Molecular mass of nitrogen is known as

The root mean square speed of nitrogen is given by the expression,

Where,

R = universal gas constant having value

Hence,

On calculation, we get,

= 508.26 m/s

The mean free path (l) is given by relation:

Where,

is the Boltzmann constant having value

So,

We get,

Collision frequency

On calculation,

On calculation, we get

On further calculation, we get

Time taken between successive collisions:

Hence,

On calculation, we get,

= 500

As a result, the time taken between successive collisions is 500 times the time taken for a collision.