If two parallel metal plates separated by a small gap are charged, one positively and one negatively, then there will be an electric field between the plates. If the electric field is larger than a certain threshold, then a spark may jump across the gap, partially discharging the plates. The threshold electric field depends on the type and pressure of the gas between the plates.
To see how a spark occurs, imagine a lone electron between the plates. It experiences a force and an acceleration, so it will move in the direction of the positive plate. Before it gets there, it is likely to collide with a gas particle. The average distance an electron travels before encountering a gas particle is the mean free path. The mean free path depends only on the number density of the gas, that is, the number of gas particles per unit volume. If the electron gains enough energy before colliding with the gas particle to ionize it, then after the collision there are more electrons to continue the process. The original electron loses much of its kinetic energy but is still available to accelerate and ionize other gas particles. (See figure.)
A lone electron thus undergoes acceleration and energy gain, followed by a collision, depositing energy into the gas particle and debris. Each collision releases several electrons, so the phenomenon grows exponentially. The process described is a run-away chain reaction. The result is a transfer of charge from one plate to the other. In addition, the discharge leaves many molecules in an excited state, which releases photons as they decay to the ground state.
For air at atmospheric pressure the threshold electric field is about
Eth = 3 x 106 N/C
You may also use the following:
r0 = the average atomic radius = 6 x 10–11 meters
lmfp = the mean free path = 8 x 10–9 meters
How much force would a calcium atom experience if it were between the plates? (Assume the electric field is the threshold electric field for air.)