How to Calculate Likelihood of Electron Jumping a Gap in Air?

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liquidFuzz
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I'd like to calculate the likeliness of an electron jumping a gap of 100 to 200 nm. I have a source emitting electrons, the potential is 10 - 20 V. What is the proper way of calculate this?

[itex]\displaystyle N = N_0 e ^{-?}[/itex] where [itex]N_0[/itex] is the amount of emitted electrons. If I use this way, how do I determine the speed of the decline, in other words the exponent in the formula?
 
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You may want to look up the mean free path of an electron in a STP air.

Note that the mean free path may also be dependent on the energy of the electrons.

Zz.