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An electron can be thought of as a point particle with zero radius.

Find an expression for the mean free path of an electron through a gas.

The mean free path of an electron can be represented by:

[tex]\lambda = \frac{1}{\sqrt{2} \pi \frac{N}{V} r^2}[/tex]

Electrons travel through L = 3 km in the Stanford Linear Accelerator. In order for scattering losses to be negligible, the pressure inside the accerlator tube must be reduced to the point where the mean free path is at least 50 km. What is the maximum possible pressure inside the accelerator tube, assuming T = 293 K?

By using the equation [tex] \lambda = \frac{L}{N_{coll}}[/tex]

[tex] N_{coll} = \frac{L}{\lambda } = \frac{3}{50} = 0.06 collisions[/tex]

I then know that

[tex]N_{coll} = \frac{N}{V}V_{cyl} = \frac{N}{V}\sqrt{2} \pi r^2 L[/tex]

However, I don't know how to continue from here to find the pressure, because I know neither the number density [itex]\frac{N}{V}[/itex] or the radius [itex]r[/itex].

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# Mean Free Path of an Electron -

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