Modern vacuum pumps can evacuate a vessel down to a pressure of \(4.0 \times {10^{ - 15}}\, atm\) at room temperature \((300\, K)\). Taking \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) and \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) , the mean distance between molecules of gas in an evacuated vessel will be of the order of

\(Y=\frac{K T}{\sqrt{2} \pi \sigma^{2} p}\)

-wherein

\(\sigma=\) Diameter of the molecule

\(p=\) pressure of the gas

\(T=\) temperature

\(K=\) Boltzmann's Constant

Let intermolecular distance be \(D\) then in a volume \(\frac{4 \pi}{3} D^{3}\) there is only one

\(\frac{4 \pi}{3} D^{3} P=\frac{1}{N_{A}}=R_{T} \quad\) or \(\quad D=\left(\frac{3 R T}{4 \pi N_{A} P}\right)^{1 / 3}\)

\(\begin{aligned} \text { Put } P=& 4 \times 10^{-10} P a, R=83, N_{A}=6 \times 10^{23} \\ T=& 300 \mathrm{K} \end{aligned}\)

\(D=0.2 \mathrm{mm}\)