Molecules of a real gas’ are not point like particles. For simplicity, molecules are assumed to be spherical. Because of their finite size, two molecules collide with each other when they come within a molecular diameter of each other, strictly speaking, within the sphere of influence of each molecule.
The molecular collisions, though perfectly elastic, result in significant changes in the speeds and
Brownian motion of a gas molecule
directions of motion of the molecules. Hence, every molecule follows a zigzag path, with abrupt changes in its speed and direction of motion at short and random time intervals. This is called Brownian motion.
Free path : The straight line path of a molecule, i.e., the distance covered by it between successive collisions, is called a free path.
Mean free path : The average distance travelled by a gas molecule between successive collisions, the average being taken over a large number of free paths (or collisions) is called the mean free path.
Maxwell, on the basis of the law of distribution of molecular speeds, obtained the formula for the mean free path (λ) as λ = \(\frac{1}{\sqrt2\pi d^2(N/V)}\), where N is the number of molecules in volume V of the gas and d is the diameter of a molecule.
[Note : Brownian motion is named after Robert Brown (1773-1858), British botanist, who, in 1827, observed under the microscope the random movement of pollen grains suspended in water.]
