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Re: [Phys-L] mean free path for electrons vs. air molecules



I note that in the Wikipedia article about mean free path (
http://en.wikipedia.org/wiki/Mean_free_path) the figure of 69 nm indeed
refers to the random motion of molecules whose speed distribution is
Maxwellian.

In our own textbook we make an estimate for an electron's mean free path to
be about 500 nm (0.5 micron), using the simple model of considering a
cylinder whose radius is related to molecular sizes and whose length is
such that on average it contains one molecule to be hit, in which case
we'll say that the length represents the mean free path. We end up with an
estimate for the breakdown strength of air being 3e7 V/m, which is off by
an order of magnitude from the observed value of 3e6 V/m. Not great
agreement, but it's a very simple model, among which simplifications it
assumes essentially that all electrons are accelerated through one mean
free path before colliding, not more distance than that. Etc.

Despite being off by an order of magnitude, this model for initiating a
spark works a lot better than the intuitively appealing notion that you
need a field strong enough to yank electrons out of molecules, for which a
simple estimate gives a critical field strength of 1e11 V/m!

Bruce