Kinetic diameter is a measure applied to

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

s and

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

s 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 In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (o ...

, 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 Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

event. Kinetic diameter is related to the

mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

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,Ismail ''et al.'', p. 14 :

d^2 =

:where, :''d'' is the kinetic diameter, :''r'' is the kinetic radius, r = d/2, :''l'' is the mean free path, and :''n'' is the

number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...

of particles 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 In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used ...

of energies must be considered, which leads to the modified expression, :

d^2 =

List of diameters

The following table lists the kinetic diameters of some common molecules;

Dissimilar particles

Collisions between two dissimilar particles occur when a beam of fast particles is fired into a gas consisting of another type of particle, or two dissimilar molecules randomly collide in a gas mixture. For such cases, the above formula for scattering cross section has to be modified. The scattering cross section, σ, in a collision between two dissimilar particles or molecules is defined by the sum of the kinetic diameters of the two particles, :

\sigma = \pi (r_1 + r_2)^2

:where. :''r''₁, ''r''₂ are, half the kinetic diameter (ie, the kinetic radii) of the two particles, respectively. We define an

intensive quantity Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is on ...

, the scattering coefficient α, as the product of the gas number density and the scattering cross section, :

\alpha \equiv n \sigma

The mean free path is the inverse of the scattering coefficient, :

l =  =

For similar particles, ''r''₁ = ''r''₂ and, :

l =  =  =

as before.Freude, pp. 3-4

References

Bibliography

*Breck, Donald W., "Zeolite Molecular Sieves: Structure, Chemistry, and Use", New York: Wiley, 1974 . *Freude, D., ''Molecular Physics''
chapter 2
2004 unpublished draft, retrieved an
archived
18 October 2015. *Ismail, Ahmad Fauzi; Khulbe, Kailash; Matsuura, Takeshi, ''Gas Separation Membranes: Polymeric and Inorganic'', Springer, 2015 . *Joos, Georg; Freeman, Ira Maximilian, ''Theoretical Physics'', Courier Corporation, 1958 . *Li, Jian-Min; Talu, Orhan, "Effect of structural heterogeneity on multicomponent adsorption: benzene and p-xylene mixture on silicalite", in Suzuki, Motoyuki (ed), ''Fundamentals of Adsorption'', pp. 373-380, Elsevier, 1993 . *Matteucci, Scott; Yampolskii, Yuri; Freeman, Benny D.; Pinnau, Ingo, "Transport of gases and vapors in glassy and rubbery polymers" in, Yampolskii, Yuri; Freeman, Benny D.; Pinnau, Ingo, ''Materials Science of Membranes for Gas and Vapor Separation'', pp. 1-47, John Wiley & Sons, 2006 {{ISBN, 0470029048. Molecular physics