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 ).

Answer:

Mean free path

Collision frequency

Successive collision time

Pressure inside the cylinder containing nitrogen,

Temperature inside the cylinder,

Radius of a nitrogen molecule,

Diameter,

Molecular mass of nitrogen,

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

Where,

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.