[QUE/QM-07005]

In the classical kinetic theory of gases, molecules are assumed to be point  particles ( of rigid shapes) in motion. Assume the average kinetic energy of the  molecules to be ${3\over 2} kT$. Using the uncertainty principle, estimate the  minimum uncertainty in position of a molecule. Compare this with average molecular distance for a gas of density $\rho$ ( $\rho=N/V$ , $N=$ number of  molecules and $V=$ volume )  When do the quantum mechanical effects become  significant ? Estimate this temperature for (a) He gas at normal pressure (b) an electron gas at density of $2.5 \times 10^{22} $ electrons/cc.