Write the assumptions made by Maxwell to derive the expression for distribution function of velocities. Hence derive the expression of Maxwellian distribution function for molecular speeds. Plot Maxwellian distribution function as a function of molecular speed.

In deriving the expression for the distribution function of velocities, Maxwell made a number of key assumptions:

1. Ideal Gas Behavior: The gas consists of a large number of identical molecules that do not interact with each other except for elastic collisions. These collisions are brief and do not result in energy exchange.

2. Statistical Approach: The system is assumed to be in equilibrium, meaning the properties of the gas are not changing over time. The distribution of molecular speeds is a result of the random motion of molecules in the gas.

3. Isotropy of Molecular Velocities: The gas is assumed to be _________ ________ _________ _________ ________ ________.
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