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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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}{\sqrt{2}n\sigma}, \end{split} \end{align} which…
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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/photons is 300,000 km/second?
user280085
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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 droplets in the air. The official solution is: If…
M. A.
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Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
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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 concepts that would be even better. I'd like to…
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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 me. aboveL An example of the universal curve…
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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 density (assumed to be homogeneous) and $\sigma$ is…
Riemann
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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. Paik, Is the mean free path the mean of a…
Andrew Steane
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Formula for mean free path in two dimensions

I'm running some simulations of particle collisions in two dimensions with discretised time and space. In essence, particles only collide if they occupy the same location (cell) at the same time step. The particles are in a 2D box and collide with…
4
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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 the mean free path of a phonon? I know that…
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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 frame $A$. There is an inertial frame $B$ which is…
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RMS Free Path vs Mean Free Path

I am trying to determine the mathematical difference between mean free path and root-mean-square free path. For an ideal gas, the relaxation time is $$\tau=\frac{1}{\sqrt2 \pi nd^2 \bar v}$$ and the mean free path is $$\Lambda=\tau \bar v $$ so the…
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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 whether or not those definitions are the same or…
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Mean free path of UV photon

I was wondering if there's a simple way to compute the mean free path of UV photons in a optically thick medium with density n. I've looked up at the literature and found out that the mean free path of Lyman-Werner band photon is ~1 Mpc on…
Brian
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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 charge exchange cross-section at a given ion…
auden
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