The expression for the mean free path in a gas of a particle with radius r is
in which N is the number of molecules, and V is the volume, and the factor of √2 in the denomiator accounts for the motion of the oncoming particles in the gas. Electrons can be thought of as point particles with zero radius.
Electrons travel 3 km through the Stanford Linear Accelerator (SLAC). In order for
scattering losses to be negligible, the pressure inside the accelerator tube must be reduced to the point where the mean free path of the electrons is at least 50 km. What is the maximum possible pressure inside the tube, assuming T=50 C? Give your answer in Pascals.
a) None other than the one above.
The Attempt at a Solution
The model used to describe mean free path is the number of molecules within a cylinder of radius r swept out by a particle over a distance v*t. The number of molecules within the cylinder = number of collisions. However, since electrons have no radius, I'm not sure where to go from here. The "cylinder" would have to be infinitely small, hence no collisions, and an infinite mean free path. The SLAC is filled with He or N2, can't remember which, but putting in the radius for one of these molecules doesn't seem correct to me. The second part is easy enough, but I am absolutely stuck on the first half. Any help is appreciated.