NCERT Class 11 Physics Solutions: Chapter 13 – Kinetic Theory-Part 5

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Question 13.10:

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


Mean free path

Collision frequency

Successive collision time

Pressure inside the cylinder containing nitrogen,

Temperature inside the cylinder,

Radius of a nitrogen molecule,


Molecular mass of nitrogen,

The root mean square speed of nitrogen is given by the relation:


is the universal gas constant

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

Where, is the Boltzmann constant

Collision frequency

Collision time is given as:

Time taken between successive collisions:

Hence, the time taken between successive collisions is the time taken for a collision.