Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17 °C. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of N₂ = 28.0 u).

Mean free path = 1.11 × 10^–7 m
Collision frequency = 4.58 × 10⁹ s^–1 

Successive collision time ≈ 500 × (Collision time) 
Pressure inside the cylinder containing nitrogen,

 P = 2.0 atm
    = 2.026 × 10⁵ Pa 
Temperature inside the cylinder, T = 17°C =290 K 
Radius of a nitrogen molecule, r = 1.0 Å
                                                = 1 × 10¹⁰ m 
Diameter, d = 2 × 1 × 10¹⁰ = 2 × 10¹⁰ m 
Molecular mass of nitrogen, M = 28.0 g
                                             = 28 × 10^–3 kg 
The root mean square speed of nitrogen is given by the relation,

Collision frequency =  
                             = 508.26 / (1.11 × 10^-7) 
                             =  4.58 × 10⁹ s^-1 

Collision time is given as, 
T = 

  =  
  =  3.93 × 10^-13 s
Time taken between successive collisions, 
T ' = l / v_rms 
    = 1.11 × 10^-7 / 508.26 
    =  2.18 × 10^-10 s
Therefore, 
 
Hence, the time taken between successive collisions is 500 times the time taken for a collision.