Pauli Exclusion Principle?

Question

A sample of 1.00 x 10^8 hydrogen atoms confined to a cubical volume of 1.00 x10^-9 m^3 and at a temperature of 2.00 x 10^-8 K mass of the hydrogen atom 1.673 x 10^-27Kg

Can someone explain what happens as the gas above is cooled to below the temperature where indistinguishability becomes important?

I think it is to do with the fact it is a fermion gas and it obey's the Pauli Exclusion Principle

Answer 1

Pauli Exlusion principle states that no two entities can occupy the same exact space at the same time if they have the same density.Gas expands as a function of temperature and at the same time its atoms increase in volume.
If the Gas is cooled it volume theoretically decreases and as its temperature aproaches zero its volume should be zero.
However its not exactly true because as a gas is cooled to vely low temperature it changes phase and becomes a liquid.
At Zero degrees absolute the Gas would be solid and Its atoms are packed to a limit where they cannot occupy a smaller volume. This is the limit condition which I Call a "Frozen Atom." At this point a repulsion occurs between the atoms. The Reason is because the substance of space between the atoms becomes so compressed that a Pressure of Repulsion is born that keeps the atoms at bay. Never the less the Atom retains its integrity with its Electron now moving at the speed of light.

Its very vely simple

Answer 2

Pauli Exclusion Principle.

Answer 3

Bose-Einstein condensation.