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(B) The mean distance $D$ between gas molecules is related to the number density $n$ by the relation $D \approx n^{-1/3}$.From the ideal gas law,$PV =

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$0.2 \, mm$

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(B) The mean distance $D$ between gas molecules is related to the number density $n$ by the relation $D \approx n^{-1/3}$.From the ideal gas law,$PV = n_{mol}RT$,where $n_{mol} = N/N_A$.Thus,$P = (N/V) \cdot (R/N_A) \cdot T = n \cdot k_B \cdot T$,where $n = N/V$ is the number density.Given $P = 4.0 	imes 10^{-15} \, atm = 4.0 	imes 10^{-15} 	imes 10^5 \, Pa = 4.0 	imes 10^{-10} \, Pa$.Using $n = P / (k_B T)$,where $k_B = R/N_A = 8.0 / (6 	imes 10^{23}) \approx 1.33 	imes 10^{-23} \, J/K$.$n = (4.0 	imes 10^{-10}) / (1.33 	imes 10^{-23} 	imes 300) = (4.0 	imes 10^{-10}) / (4.0 	imes 10^{-21}) = 10^{11} \, molecules/m^3$.The mean distance $D \approx n^{-1/3} = (10^{11})^{-1/3} \approx 10^{-3.66} \, m \approx 2.15 	imes 10^{-4} \, m = 0.215 \, mm$.Thus,the order of magnitude is $0.2 \, mm$.

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