Modern vacuum pumps permit to pressures down to `p = 4.10^-15 atm` to be reached at room temperatures. Assuming that the gas exhausted is nitrogen, find the number of its molecules per `1 cm^3` and the mean distance between them at this pressure.

Explanation

From the formula `p = n k T`
`n = (p)/(kT) = (4 xx 10^-15 xx 1.01 xx 10^5)/(1.38 xx 10^-23 xx 300) per m^3`
=`1 xx 10^11 per m^3 = 10^5 per c.c`
Mean distance between molecules
`(10^-5 c.c)^(1//3) = 10^(1//3) xx 10^-2 cm = 0.2 mm`.