Question

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

Answer 1

The mean free path is given by

where k = Bottzmann constant

= 1.38 × 10^-23kg²m²s^-2k^-1

d = diameter of the atom / molecule

= 2 × 1 Å = 2 × 10^-10 m

P = Pressure of the gas = 2 atm

2.026 × 10⁵ Pa

= 11.12 × 10^-8 m

= 1.112 × 10^-7 m

∴ mean free path = 1.112 × 10^-7 m 

RMS speed of nitrogen molecules is given by

∴ collision frequency, f = V_rms/l

= 3.935 × 10^-13 s.

Time gap between successive collisions,

∴ the time taken between successive collisions is about 500 times the time spent on collision.