What is the amount of ? The number of ionization depends upon the probability that an electron hits a gas molecule.  This probability  is the relation of the cross-sectional area of a collision between electron and ion  in relation to the overall area  that is available for the electron to fly through:
As expressed by the second part of the equation, it is also possible to express the probability as relation of the path traveled by the electron  to the mean free path  (distance at which another collision occurs).
 is the number of molecules which electrons can hit.  It can be calculated using the equation of state of the ideal gas
:: pressure, : volume, : Boltzmann constant, : temperature)</small>
The adjoining sketch illustrates that .  As the radius of an electron can be neglected compared to the radius of an ion  it simplifies to . Using this relation, putting () into () and transforming to  one gets
where the factor  was only introduced for a better overview.
The alteration of the current of not yet collided electrons at every point in the path  can be expressed as
This differential equation can easily be solved:
The probability that  (that there was not yet a collision at the point ) is
According to its definition  is the number of ionizations per length of path and thus the relation of the probability that there was no collision in the mean free path of the ions, and the mean free path of the electrons:
It was hereby considered that the energy  that a charged particle can get between a collision depends on the electric field strength  and the charge :