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Questions tagged [mean-free-path]

The average length that a molecule will travel in a fluid before colliding with another molecule.

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Mean free path equation for plasma

Does the mean free path equation $$\lambda=\frac{1}{\sqrt{2}\pi d^2 n_v}$$ work for collisions in plasma or just for gas?
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Predicting electrical mean free path in nanostructures?

How does one roughly predict the mean free path for electrical conduction in a nanostructure at different temperatures and under different electrical conditions such as different voltages and ...
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Standard deviation for a free path distribution

I would like to be able to describe a particles path before collisions with greater precision. We can calculate the "mean" free path of a particle before colliding moving particles, but I ...
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How is number of collisions per unit distance related to mean free path?

Recently I have been studying Kinetic Theory Of Gases, with one of the topics as collision frequency. I know that collision frequency is inverse of relaxation time which is also the measure of number ...
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Determining the single particle energies in a neutrino opacity calculation

I'm attempting to recreate some plots from this paper on neutrino opacity calculations for interacting matter at supra-nuclear densities. Namely, I'm trying to write a Python script to perform the ...
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Why does computing mean free path from an air molecule's reference frame seem to greatly overestimate path length?

I was interested in seeing if I could derive the mean free path of an "air molecule" by considering the reference frame of an individual molecule as other particles moved around it randomly. ...
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Number of fog droplets in the air

I have an issue with the official solution to this problem from BelPhO: Visibility on the road is 100 m. Assuming that the diameter of a fog droplet is 1 micron, estimate the concentration of fog ...
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Mean free path of molecules

So in the book concepts in thermal physics(by Stephan and Katherine Blundell) the expression of mean scattering time is derived as shown(please refer the book for more). If we replace vdt in the ...
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Why is the sphere of influence of the molecule in mean free path a cylinder?

In my book for deriving mean free path a cylinder is taken to act as a sphere of influence of molecules with which it could bump into other molecules and its radius = diameter of the molecule we are ...
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How does $\frac{\langle v\rangle}{\langle v_r\rangle}=\frac{1}{\sqrt2}$ imply the formula for the mean free path?

In this question, it was asked how the formula $$l=\frac{1}{\sqrt 2n\sigma }$$ can be rigorously derived for a Maxwell-Boltzmann gas. Here $l$ is the mean free path length in a gas, $n$ is the gas ...
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Free Path Probability Distribution for an Ideal Gas

Suppose we have a gas with collisions. The mean free path, $l$, is the average distance a particle travels before colliding with another particle. This is the average, but what is the probability ...
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Question regarding correction factor in Mean free path

1)The expression for $Mean$ $Free$ $Path$ (ie) , $$λ=\dfrac{1}{πd²\dfrac{n}{V}}$$ is derived under the assumption that the particles except the one( let's consider it as particle $A$) you're ...
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Collisional cross-section from attenuation factor

I am trying to find the mean free path of silver atoms travelling through air (I am given the temperature, pressure and that they are attenuated by a factor $2.72$ in a distance of $10^{-2}$m). I know ...
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Mean free path regarding billiards

Is there a generalization of the mean free path for macro-objects such as the distance the white billiard ball could travel before hitting an other billiard ball?
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Ratio of mean free paths between two equal volumes at different temperature, separated by a partition with pinhole

Question: A container is divided into two equal parts I and II by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_I$​= ...
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What does ultra-rarefied gas mean?

Without using any math, can you explain to me what a rarefied gas is? And then what an ultra-rarefied gas is? I'd like to understand it from a conceptual level if you can make connections to other ...
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Which average are we taking in a rigorous calculation of the mean free path in a gas?

This is a question at one level beyond the standard introductions to kinetic theory. I want to know which average we are taking when we talk about a mean free path in a gas. I recently read Steve T. ...
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Why is mean free path independent of mass?

In this page of Hyperphysics, I am puzzled as to why there isn't any mass dependence in the expressions for mean free path. Here are the two equations as mentioned in the website: When only one ...
Cathartic Encephalopathy's user avatar
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Why is the mean free path length of an electron in a solid described by a "universal curve"? (doesn't include electron density)

I've been experimenting with XPS (X-ray photoelectron spectroscopy) and learned that the depth from which the observed electrons originated depends on their mean free path length, which makes sense to ...
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How to calculate the free mean path of electrons in the gas mixture? [closed]

How to calculate the free mean path of electrons in the gas mixture? I understand (a little bit) the mean free path concept for the atomic collisions but I am not sure what to do if I am interested in ...
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What is the mean free path (MFP) of a Cosmic microwave background radiation (CMBR) photon?

If the IGM (inter-galactic medium) had a massive particle (proton) every cubic metre, or a carbon grain every cubic kilometre, what would be the MFP of a CMBR photon? The coherence length of the ...
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How can mean free path affect the propagation of sound in a gas?

I was thinking, since mean free path is a measure of "how long" a particle has to travel to collide with another, that this surely must influence sound propagation somehow. I would say this ...
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What does this equation represent?

While doing the Franck-Hertz experiment I noticed that I have been asked to write the current as a function of the Mean Free Path as following: $$ I=a\cdot e^{-\frac{b}{\lambda}}$$ I- current $\lambda$...
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Franck Hertz experiment and the Mean Free Path

As part of my project in physics, I tried to repeat the franck hertz experiment, I did the same experiment with Neon and Mercury (the lengh between the catode and lattice is $5 mm$), I measured the ...
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Infering the mean distance from density

A simple calculation surely but how we can infer the mean distance $l_{\text{mean}}$ between particles from their density $n$, i.e : $$l_{\text{mean}}=\left(\dfrac{1}{n}\right)^{1/3}$$ ? I tried to ...
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Monte Carlo approach to determining mean free path of Lévy dust

Problem statement I am trying to determine the mean free path $\lambda$ of a so-called Lévy dust, i.e. $M$ points in a square $L\times L$ environment with distances between subsequent points ...
Johannes Nauta's user avatar
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In particle physics what is the derivation of the mean free path length: $\ell=\frac{1}{n \sigma}$?

From my lecture notes (ICL, dept. of Physics) it is written: Consider a thin piece of material with thickness $d$ containing target particles with number density $n$, as illustrated in Figure $\bf{2....
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Do photons slow down this much in the Sun's gravitational field?

I just heard someone mention that photons take 40 thousand years to travel from the centre of the Sun to its surface which is roughly 700,000 kilometres. How is that possible if the speed of light/...
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How to calculate the mean free time in Drude model?

According to Drude model, the average electron takes some time to go from one ion to another: this time is called mean free time. The problem is there isn't a satisfactory definition of this mean free ...
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Why does thermal conductivity decrease from solids to gases?

I am learning in my heat transfer class that the thermal conductivity decreases from solids to liquids to gases i.e. $$K_{solid} > K_{liquid}>K_{gas}$$ The reason cited is that (based on my ...
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Mean free path of electron in air?

I'm interested in approximating the mean free path of an electron in air. I think I'm going to need to add something more into my approximation because currently I calculate $400m$ for the mean free ...
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Two versions of Diffusion coefficient

I found two versions of the Diffusion coefficient, first: $$D=\frac{\pi \lambda }{8}\overline{c}$$ Where $ \overline{c}$ ist the particles mean thermal velocity and $\lambda$ the particles mean free ...
Gustaf Oberst Stôlgeng's user avatar
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Usually, how much does a phonon travel without scattering?

Phonons propagate without problems in a lattice, until they scatter on something, like a defect, an electron, or another phonon. But in a typical solid at room temperature, how much (or how long) is ...
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Mean free path for charged molecule inside air

Question I would like to compute the mean free path ($\lambda$) for a "heavy" charged molecule ($M$amu, $q$ charge) in a low pressure gaz (air, but also ions such as Ca$^+$). I think I figured out ...
Aldehyde's user avatar
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The mean free path of electrons in high vacuum is 26 billion kilometres?

I used this formula to calculate the mean free path length of an electron in high vacuum. $$\lambda = \frac{k T}{\sqrt{2}\cdot4\pi r^2 \cdot p}$$ where k is the Boltzmann konstant, T the temperature ...
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How to (hypothetically) calculate $\tau$, the mean free time?

Referring to the Drude Model, I've seen a lot of excellent questions on whether $\tau$ should be thought of as the "average time between collisions" or the "average time until the next collision", and ...
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Electron mean free path as a function of pressure

How do I calculate electron beam mean free path as a function of vacuum pressure? For example, if I am pumping a vacuum system down and have an electron beam of known energy, what is the mean free ...
Jeremy Adams's user avatar
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3 answers
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Rigorous derivation of the mean free path in a gas

Can anyone supply me with a derivation of the mean free path, of particles in a Maxwell Boltzmann Gas? Cited in various literature is the formula, \begin{align} \begin{split} \ell&=\frac{1}{\...
user400188's user avatar
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Mean free path for $3\rightarrow 1$ scattering

I want to calculate the mean free path of an antineutrino in nuclear matter where it can undergo the reaction $p+e^-+\bar{\nu} \rightarrow n$, which I imagine will involve calculating the rate of that ...
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Most probable free path length

The distribution of scattering time is $nv\sigma e^{-nv\sigma t}$ where $\sigma$ is the collision-cross section, $n$ is the number density of molecules and $v$ is the average relative velocity. This ...
hola's user avatar
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How is the waveform deviation from the equilibrium related to the air molecule movement?

I'm not sure if this is a stupid question. I've been considering the deviation from the equilibrium reflects the air pressure, with larger deviations reflecting higher air pressure. But in Reetz and ...
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Average distance travelled before absorbtion 253 nm photon in air

At first I wanted to use term "Mean free path" in title but I know it means other kinds of interactions too,not just absorbtion.What I really mean is mean free path but only for absorbtion. For ...
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How to interpret 'electron energy above fermi level (eV)'?

In some mean free path graphs, I see 'electron energy above Fermi level (eV)' on the x-axis See figure: What does it mean? Is it electrons kinetic energy in the material? What happens if the graph ...
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Mean free path of gas mixture

I come cross a question about calculate the MFP of a gas mixture, which contains several different kinds of molecules, each has different size, velocity and number density. My question is: How can I ...
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Is penetration of a fast particle deep into a medium a quantum mechanical effect?

Consider the cosmic rays. The muons can travel 15000 meters through the atmosphere and get down to sea level. If this is not a quantum mechanical effect, its penetration depth is determined by the ...
Jiang-min Zhang's user avatar
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390 views

Ion charge exchange mean free path

I am using the following equation to calculate the mean free path between a deuteron ion and background gas: $$\lambda_{d-gas} = \frac{kT_{gas}}{p_{gas} \, \sigma_{10}}$$ Where $\sigma_{10}$ is the ...
auden's user avatar
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Viscosity and mean free path

I have troubles understanding how to derive the formula for viscosity in terms of the mean free path $$\eta\sim \rho \lambda \bar v$$ where $\bar v$ is the average molecular velocity of the gas, $\...
Jonathan Lindgren's user avatar
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speed distribution and mean free path of gases at pressure

I know that at 18,000 ft. above mean sea level, the atm. pressure ~half of what it is at seal level (760 Torr). The temperature also decreases by 70C. a. How would this change the speed distribution ...
Jackson Hart's user avatar
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1 answer
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Mean free path in 2d? [duplicate]

Let us say we have a collection of $n$ stationary balls per square meter each of diameter $d$ and we roll an identical ball between them. Then what is the free mean path of this ball? My ...
Quantum spaghettification's user avatar
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1 answer
390 views

Derivation of relativistic mean free path

I am working through a short derivation found in Abramowicz 1991 regarding the mean free path of a photon. We have a fluid moving in a particular direction with velocity $v$ and in an inertial rest ...
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