# Mean free path of electron in gas.

• lacunae
Stanford Linear Accelerator. In summary, the mean free path for electrons in a gas is affected by the number of molecules, volume, and the motion of oncoming particles. For electrons to travel 3 km through the SLAC without significant scattering losses, the pressure inside the accelerator must be reduced to a point where the mean free path is at least 50 km. Assuming a temperature of 50°C, the maximum possible pressure inside the tube can be calculated using the ideal gas law.

## Homework Statement

The expression for the mean free path in a gas of a particle with radius r is
((N/V)*pi*r^2*4*(2)^.5)^-1
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.

## Homework Equations

a) None other than the one above.
b) PV=NkT

## 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.

If the electron approximates an atom within the radius of the atom they will collide. You can imagine that the electron carries the scattering cross section instead of the atoms and the atoms of the gas are stationary points inside the cylinder.

ehild