The Kinetics of Collision and Ionization

The Kinetics of Collision and Ionization.—In the last section we have been considering the emission and absorption of radiation as a mechanism for the transfer of atoms or molecules from one energy level to another. The other important mechanism of transfer is that of collisions with another atom, molecule, or more often with an electron. In such a collision, the colliding particles can change their energy levels, 

In a similar way, in the atomic or molecular case, we allow a beam of colliding particles to strike the atoms or molecules that we wish to investigate. A certain number of the particles in the incident beam will pass by without collision, while a certain number will collide and be deflected. We count the fraction colliding, divide this fraction by the number of particles with which they could have collided, and the result is the collision cross section. This can plainly be made the basis of an experimental method of measuring collision cross sections. We start a beam 

Let the beam have unit cross section, and let a be a coordinate measured along the beam. The intensity of the beam, at point x, is defined as the number of particles crossing the unit cross section at x per second. We shall call it I x), and shall find how it varies with x. Consider the collisions in the thin sheet between x and x + dx. Let the number of particles per unit volume with which the beam is colliding be N/V. Then in the thin sheet between x and x + dx, with a volume dx, there will be N dx/V particles. Let each of these have collision cross section A. Then the fraction of particles colliding in the sheet will by definition be NA dx/V. This is, however, equal to the fractional decrease in intensity of the beam in this distance. That is, 

From Eq. (3.3) we see the exponential decrease of intensity of which we have just spoken, and it is clear that by measuring the rate of exponential decrease we can find the collision cross section experimentally. 

The intensity of a beam falls to 1/e of its initial value, from Eq. (3.3), in a distance 

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