Kinetic diameter is a measure applied to atoms and molecules that expresses the likelihood that a molecule in a gas will collide with another molecule. It is an indication of the size of the molecule as a target. The kinetic diameter is not the same as atomic diameter defined in terms of the size of the atom's electron shell, which is generally a lot smaller, depending on the exact definition used. Rather, it is the size of the sphere of influence that can lead to a scattering event.
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Kinetic diameter is related to the mean free path of molecules in a gas. Mean free path is the average distance that a particle will travel without collision. For a fast moving particle (that is, one moving much faster than the particles it is moving through) the kinetic diameter is given by,
However, a more usual situation is that the colliding particle being considered is indistinguishable from the population of particles in general. Here, the Maxwell–Boltzmann distribution of energies must be considered, which leads to the modified expression,
List of diameters
The following table lists the kinetic diameters of some common molecules;
Dissimilar particles
The colliding particle may be a different molecule to the molecules in the gas and hence will have a different kinetic diameter. This can occur, for instance, if a beam of fast particles is fired into the gas. The kinetic diameter defines an area, σ, called the scattering cross section. The scattering cross section in a collision is defined by the sum of the kinetic diameters of the two particles,
We define an intensive quantity, the scattering coefficient α, as the product of the gas number density and the scattering cross section,
The mean free path is the inverse of the scattering coefficient,
For similar particles, r1 = r2 and,
as before.