(a) The mean free path is the average distance a molecule travels before colliding with another molecule. The mean free path,λ, is given λ = KTI (√2σP) by where k is Boltzmann's constant, T is temperature (K), P is pressure (Pa), and is the collision cross section. For a molecule with a diameter d, the collision cross section is d. The collision cross section is the area swept out by the molecule within which it will strike any other molecule it encounters. The magnetic sector mass spectrometer is maintained at a pressure of ~10-5 Pa (~10-7 Torr) so that ions do not collide with (and deflect) one another as they travel through the mass analyzer. What is the mean free path of a molecule with a diameter of 1 nm at 300 K in the mass analyzer?
(b) The vacuum in an orbitrap mass separator is ~10-8 Pa (~10-13 bar, ~10-10 Torr). Find the mean free path in the orbitrap for the same conditions as (a).