Editing Mean free path (section)

==In other fields==
===Radiography===
[[File:Photon Mean Free Path.png|thumb|right|400px|Mean free path for photons in energy range from 1 keV to 10 MeV for elements with [[Atomic number|''Z'']] = 1 to 100.<ref>Based on data from {{cite web |date=1998-03-10 |title=NIST: Note - X-Ray Form Factor and Attenuation Databases |url=https://physics.nist.gov/PhysRefData/XrayNoteB.html |access-date=2011-11-08 |website=Physics.nist.gov |publisher=}}</ref> The discontinuities are due to low density of gas elements. Six bands correspond to neighbourhoods of the [[w:noble gas|noble gases]] (<sub>2</sub>He, <sub>10</sub>Ne, <sub>18</sub>Ar, <sub>36</sub>Kr, <sub>54</sub>Xe, <sub>86</sub>Rn). Also shown are locations of [[absorption edge]]s: K,L,M,N-shell electrons. Logarithmic scale 0.1 μm-1 km]]

In [[gamma-ray]] [[radiography]] the ''mean free path'' of a [[pencil beam]] of mono-energetic [[photon]]s is the average distance a photon travels between collisions with atoms of the target material. It depends on the material and the energy of the photons:

:<math>\ell = \mu^{-1} = ( (\mu/\rho) \rho)^{-1},</math>

where ''μ'' is the [[linear attenuation coefficient]], ''μ/ρ'' is the [[mass attenuation coefficient]] and ''ρ'' is the [[density]] of the material. The [[mass attenuation coefficient]] can be looked up or calculated for any material and energy combination using the [[National Institute of Standards and Technology]] (NIST) databases.<ref name=NIST1>{{cite web
 |last=Hubbell |first=J. H.
 |author1-link=John H. Hubbell
 |last2=Seltzer |first2=S. M.
 |title=Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients
 |publisher=[[National Institute of Standards and Technology]]
 |url=http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html
 |access-date = 19 September 2007}}</ref><ref name=NIST2>{{cite web
 |last=Berger |first=M. J.
 |last2=Hubbell |first2=J. H. |author2-link=John H. Hubbell |first3=S. M. |last3=Seltzer |first4=J. |last4=Chang |first5=J. S. |last5=Coursey |first6=R. |last6=Sukumar |first7=D. S. |last7=Zucker
 |title =XCOM: Photon Cross Sections Database
 |publisher =[[National Institute of Standards and Technology]] (NIST)
 |url =http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html
 |access-date = 19 September 2007}}</ref>

In [[X-ray]] [[radiography]] the calculation of the ''mean free path'' is more complicated, because photons are not mono-energetic, but have some [[Frequency distribution|distribution]] of energies called a [[spectrum]]. As photons move through the target material, they are [[attenuation|attenuated]] with probabilities depending on their energy, as a result their distribution changes in process called spectrum hardening. Because of spectrum hardening, the ''mean free path'' of the [[X-ray]] spectrum changes with distance.

Sometimes one measures the thickness of a material in the ''number of mean free paths''. Material with the thickness of one ''mean free path'' will attenuate to 37% (1/[[e (mathematical constant)|''e'']]) of photons. This concept is closely related to [[half-value layer]] (HVL): a material with a thickness of one HVL will attenuate 50% of photons. A standard x-ray image is a transmission image, an image with negative logarithm of its intensities is sometimes called a ''number of mean free paths'' image.

===Electronics===
{{See also|Ballistic conduction}}

In macroscopic charge transport, the mean free path of a [[charge carrier]] in a metal <math>\ell</math> is proportional to the [[electrical mobility]] <math>\mu</math>, a value directly related to [[electrical conductivity]], that is:
:<math>\mu = \frac{q \tau}{m} = \frac{q \ell}{m^* v_{\rm F}},</math>

where ''q'' is the [[elementary charge|charge]], <math>\tau</math> is the [[mean free time]], ''m<sup>*</sup>'' is the [[Effective mass (solid-state physics)|effective mass]], and ''v''<sub>F</sub> is the [[Fermi velocity]] of the charge carrier. The Fermi velocity can easily be derived from the [[Fermi energy]] via the non-relativistic kinetic energy equation. In [[thin film]]s, however, the film thickness can be smaller than the predicted mean free path, making surface scattering much more noticeable, effectively increasing the [[resistivity]].

[[Electron mobility]] through a medium with dimensions smaller than the mean free path of electrons occurs through [[ballistic conduction]] or ballistic transport. In such scenarios electrons alter their motion only in collisions with conductor walls.

===Optics===
If one takes a suspension of non-light-absorbing particles of diameter ''d'' with a [[volume fraction]] ''Φ'', the mean free path of the photons is:<ref>{{cite journal
 |last1=Mengual |first1=O.
 |last2=Meunier |first2=G.
 |last3=Cayré |first3=I.
 |last4=Puech |first4=K.
 |last5=Snabre |first5=P.
 |title=TURBISCAN MA 2000: multiple light scattering measurement for concentrated emulsion and suspension instability analysis
 |journal=Talanta
 |volume=50
 |issue=2
 |pages=445–56
 |year=1999
 |doi=10.1016/S0039-9140(99)00129-0
 |pmid=18967735
}}</ref>

:<math>\ell = \frac{2d}{3\Phi Q_\text{s}},</math>

where ''Q''<sub>s</sub> is the scattering efficiency factor. ''Q''<sub>s</sub> can be evaluated numerically for spherical particles using [[Mie theory]].

===Acoustics===
In an otherwise empty cavity, the mean free path of a single particle bouncing off the walls is:

:<math>\ell = \frac{F V}{S},</math>

where ''V'' is the volume of the cavity, ''S'' is the total inside surface area of the cavity, and ''F'' is a constant related to the shape of the cavity. For most simple cavity shapes, ''F'' is approximately 4.<ref name="YoungRW">{{cite journal|last1=Young|first1=Robert W.|title=Sabine Reverberation Equation and Sound Power Calculations|journal=The Journal of the Acoustical Society of America|date=July 1959|volume=31|issue=7|page=918|doi=10.1121/1.1907816|bibcode=1959ASAJ...31..912Y}}</ref>
 
This relation is used in the derivation of the [[Reverberation|Sabine equation]] in acoustics, using a geometrical approximation of sound propagation.<ref>Davis, D. and Patronis, E. [https://books.google.com/books?id=9mAUp5IC5AMC&pg=PA173 "Sound System Engineering"] (1997) Focal Press, {{ISBN|0-240-80305-1}} p. 173.</ref>

===Nuclear and particle physics===
In particle physics the concept of the mean free path is not commonly used, being replaced by the similar concept of [[attenuation length]].  In particular, for high-energy photons, which mostly interact by electron–positron [[pair production]], the [[radiation length]] is used much like the mean free path in radiography.

Independent-particle models in nuclear physics require the undisturbed orbiting of [[nucleon]]s within the [[Atomic nucleus|nucleus]] before they interact with other nucleons.<ref>{{cite book|chapter-url=http://www.res.kutc.kansai-u.ac.jp/~cook/NVSIndex.html|title=Models of the Atomic Nucleus|last=Cook|first=Norman D.|date=2010|publisher=[[Springer Science+Business Media|Springer]]|isbn=978-3-642-14736-4|edition=2|location=Heidelberg|page=324|chapter=The Mean Free Path of Nucleons in Nuclei}}</ref>

{{Quote|text=The effective mean free path of a nucleon in nuclear matter must be somewhat larger than the nuclear dimensions in order to allow the use of the independent particle model. This requirement seems to be in contradiction to the assumptions made in the theory ... We are facing here one of the fundamental problems of nuclear structure physics which has yet to be solved.|sign=John Markus Blatt and [[Victor Weisskopf]]|source=''Theoretical nuclear physics'' (1952)<ref>{{Cite book|last=Blatt|first=John M.|last2=Weisskopf|first2=Victor F.|date=1979|title=Theoretical Nuclear Physics|language=en-gb|doi=10.1007/978-1-4612-9959-2|isbn=978-1-4612-9961-5|url=https://digital.library.unt.edu/ark:/67531/metadc1067172/}}</ref>}}