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.