Mean free path Definition and 51 Threads

I have a not-so-well based intuition about this one, I think that in general odors travel farther in winter than in summer. I can smell the close-by bakery more intensively when is cold than when is hot. This might be a variety of reasons (like there being more smells to sense in summer) but I...

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 amperages based on the composition and dimensions of the structure? For instance in carbon single and...

If the distance between the centres of two molecules is σ, then imagining a a cylinder with radius σ the number of molecules can be given by πσ²cn where c = average velocity. So mean free path can be given by λ = c/πσ²cn = 1/nπσ². But do I derive it from exp(-x/λ)?

lambda (rms)= v(rms) * t(rms) -- 1 Now I assume here that t(rms)=1/(√2*n*π*d^2*v(rms)) But this cancels the v(rms) term when used in eq (1) so the mean free path and the RMS free path would actually be the same (even later on when used in the aforementioned Survival Equation) I would like to...

We have the area of incandescence. Using that we can find the radius and subsequently the diameter. A=π* r^2 -----> r= 0.0025m so d=0.005m Using the formula (given by Clausius as we are not specified in question whether it's a Maxwellian distribution or not) Mean Free Path λ=...

I answered the first part of the question where I estimate the radius of ##O_{2}## is ##\approx 1.5 \times 10^{-10} \ \text{m}##: $$ p = \frac{KT}{l 4 \pi r^{2}} = \frac{(20+273.15)(1.38\times 10^{-23})}{(0.1)(4\pi)(1.5 \times 10^{-10})^{2}} = 0.143 \ \text{Pa}.$$ The confusion arises on the...

I used the form of the mean free path equation taking advantage of the fact that the Boltzmann constant is equal to the ideal gas constant R divided by Avogadro's number, because I didn't know if I could use the Boltzmann constant in the ##1.381\cdot 10^{-23}J/(molecules\cdot K)## form...

Are the interaction path and mean free path of a particle the same thing?

Say Temperature of a gas doubles, I do not understand how the average distance between particles (mean free path) is unaffected if they are traveling √2 times as fast in a fixed volume V. Root 2 as a factor of increase because T*2 --> KE*2 --> V*2 --> Vrms*√2 Is it because relative to one...

I have a box with a wall in mid dividing it in 2 sections, and the wall has a hole of diameter d. There is ideal gas in both sections at 150 K in one section and at 300 K in another. How am I supposed to calculate ratio of mean free paths in 2 sections. My attempt: L ~ Volume / Number of...

Per Wikipedia (Outer Space) referencing Davies, P. C. W. (1977), "...the mean free path of a photon in intergalactic space is about 10E23 km, or 10 billion light years." Per Lawrence Krauss (1999), it is longer than the size of the visible universe. What is the current thinking about this?

Homework Statement The problem that I am having stems from a problem given in the following way:[/B] "a)Show that for a gas, the mean free path ##\lambda## between collisions is related to the mean distance between nearest neighbors ##r## by the approximate relation ##\lambda \approx...

Hello everyone, I have a question regarding the implication of mean free path and pressure acoustics. I have seen several publications on the internet and also calculated the minimum displacement of a wave in air using the formula dp=v * rho * *2*pi*freq. * dx The values of displacement can...

Homework Statement The concentration of electrons per unit volume is given (atoms/m^3), temperature is also given in Kelvins (100 K). Other values were also given such as valence but I'm pretty sure that they are irrelevant. Homework Equations λ = 1/ pi * d^2 * n λ=kT/4∗π∗√2∗r^2*p The Attempt...

Homework Statement Charged pion with average life time $$\tau=10^{-8} sec$$, and mean free path in the water$$\ell=100m$$ falls prependicular to a lake (depth of lake is at $$\ell_0 =30m$$ with velocity $$V=0.9999c$$ What of the next is correct? 1). The particle isn't gona touch the bottom of...

Homework Statement A right circular cylinder of ##4## cm (inner) radius and ##19.9## cm (inner) length contains ##4 \times 10^{14}## Argon atoms (atomic number ##18##). The cylinder is maintained at room temperature, nominally ##300## K. (a) Estimate the momentum transfer per square meter per...

Homework Statement 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 of the air molecules quanitatively? b.How would it change the mean free...

What is the maximum practical or theoretical pressure at which x-rays can be produced, as in a Crookes tube or cathode ray tube? I know Crookes tubes operate at 0.1pa and lower, but I need to know if I am at risk of producing x-rays with high voltage (60kv+) discharges at medium vacuum, as low...

Homework Statement If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=360K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m−3 Homework Equations K=CVvsl l...

The sun has no surface, but it appears to have a surface. I may recall that Feynman said that the apparent diameter is equal to the mean free path of a photon. That could be, but I don't get the relationship. Any help?

My textbook says "The lower the gas pressure, the higher the mean-free-path". But it does not explain why. Can someone please explain it briefly? Thank you very much.

Is there any direct experiment to determine the value of mean free path(not the distribution) of a gas molecule?

so this is the question I'm having a little trouble with: Assume that the ratio of copper resistivity at room and absolute zero temperatures (so called "residual resistance ratio") is 1000. Estimate the electron mean free path in copper at low temperatures. we also know this: Let us assume...

Homework Statement What is the mean free path of an N2 molecule in an ultra-high-vacuum chamber at a pressure of 10-10mbar? Homework Equations λ=1/(√2)nσ number density n, collision cross-section σ p=nkT pressure p, temperature T σ=πd2 d molecular diameter The Attempt at a Solution...

http://www.pluggakuten.se/wiki/images/3/3e/Prov221.JPG Solution

Homework Statement (We are to solve this with Monte Carlo programming. Based on the universe from Olber's paradox) Suppose you are in an infinitely large, infinitely old universe in which the average density of stars is n = 10^9 Mpc^−3 and the average stellar radius is equal to the Sun’s...

I was wondering if there is a mathematical difference between the RMS free path and the mean free path of molecules in an ideal gas. For example, When I calculate the mean free path, I use use the average velocity and the scattering rate which is a function of the average velocity. I then...

Just need someone to tell me if I'm doing this right. If I have accelerated a particle in which the mean free path is 50nm and I need the collision to be 5eV would this be correct in determining the required electric field strength? 5/.00000005 = 100MV/m

Hello, Does anyone know why we use the root mean square of the relative velocity in calculating the mean free path? As is done in this example: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/MolecularCollisions.htm Seems like it would make more sense to find the mean of the...

So this is a fairly simple conceptual question: can you estimate/compare the mean free paths for individual components of a mixture of gases? I'm primarily looking at the equation given here and the information accompanying it. Consider the case where we have several individual, separate...

Hi, I have an exam tomorrow for atmospheric chemistry and I was just going over some past papers. In one it asks the following question, "What is meant by "Mean Free Path"? How is this relevant to atmospheric chemistry. My answer was as follows "The mean free path is the average distance a...

Hi, I am wondering how i can calculate the classical mean free path of electrons in InSb given the following material parameters... zero field conductivity = 1.86e4 1/ohm m electron mobility = 45,500 cm^2/Vs Is it a case of working out the scattering time and multiplying it by the...

Homework Statement If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=380K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m^{-3} Homework Equations...

The mean free path is usually determined via the scattering cross section σ; one starts with a differential equation for the intensity dI(x)= -n\,\sigma\,I(x)\,dx Are there generalizations for this derivation for energy-dependent cross sections σ(E)?

What is the Mean Free Path of water in it's liquid state? Just wondering how far an electron could travel in water before a collision?

Hello. I have just read a mean free path (a distance) written in units g/cm^2. How do you interpret this unit in terms of the usual idea of the mean free path as a distance?

Homework Statement I do need to calculate the mean free path for an ion with a radius of 9 x 10‐8 cm in pressures of 10‐8 Torr, 10‐6 Torr, 10‐4 Torr and 10‐2 Torr Homework Equations There are different equations I found but the most one is λ= 1/Nσ N gas number density which I do not...

Homework Statement Beam of silver atoms are passing through air at a temp 273K and a pressure of 1 Pa. The beam is attenuated by a factor of 2.72 in a distance of 10^-2 m. Find the mean free path of the silver atoms and estimate the effective collision radius.. Homework Equations...

A magnetic field curves the path of a charged particle for example the electron.So the application of a magnetic field should curve the path of the free electrons between successive collisions[More conspicuously for a large magnetic field].The"free path" of an electron then is no more a straight...

Homework Statement The mean free path for an ideal collisional gas can be calculated as shown on thishttp://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/menfre.html" . I understand the derivation, except for one thing. Homework Equations The Attempt at a Solution The molecule is...

Homework Statement The expression for the mean free path in a gas of a particle with radius r is ((N/V)*pi*r^2*4*(2)^.5)^-1 in which N is the number of molecules, and V is the volume, and the factor of √2 in the denomiator accounts for the motion of the oncoming particles in the gas...

I can't seem to understand the math. If I have a free electron in air, surrounded by an electric field, how do I determine and calculate the mean free path, the electric field strength, and the distance between plates required to impart an energy of 80 eV to the free electron?

Homework Statement A test tube of cylindrical shape having a length of 10 cm and a diameter of 2 cm contains 20 * 10 ^23 molecules (molecular size d = 3 * 10^-10 m). What is the mean free path of these molecules?? Homework Equations λ = 1/ pi * d^2 * n The Attempt at a Solution...

Homework Statement The resistivities and Fermi speeds of Na, Au, and Sn at T = 273 K are 4.2 µ\Omega·cm, 2.04 µ\Omega·cm, and 10.6 µ\Omega·cm, and 1.07e6 m/s, 1.39e6 m/s, and 1.89e6 m/s respectively. Use these values to find the mean free paths λ for the conduction electrons in these elements...

Homework Statement Hi, It's not a homework question, but as i am a beginner in physics, I prefer to post here first : I try to evaluate thermal resistance at low temperature. I need to compute the mean free path of both electron and phonon in metals, but I do not find any formulas. Can...

Homework Statement Hi, I am not sure about the following question: (Q) Argon (atomic weight 40) exists as a monatomic gas at room temperature and pressure. The density of liquid argon is 1784kg/m^3. (a) Calculate the atomic density (atoms/m^3) in liquid argon *Done* (b) Hence...

Homework Statement (a)What is the mean free path for oxygen molecules at 300K and atmospheric pressure (105 Pa) and the average frequency of collisions for a particular molecule? (The diameter of an oxygen molecule is 0.29 nm). (b)What is the mean free path of oxygen molecules at an...

Why is average relative velocity equal to the square root of 2 times the magnitude of the x direction velocity? I'm trying to solve some problems that deal with gas laws from Ideal gases to the Van der Waals gases. Does anybody have any ideas? Thanks.

Homework Statement My solid-state physics book (Kittel) talks about the phonon mean free path (on page 122) but never defines it. Can someone please give me a definition? I know what a mean free path is for a non-quasi-particle but I do not see how that extends to phonons. Homework Equations...

Homework Statement Neutral atomic hydrogen cloud, density n_H. Absorption cross section \sigma_{0} = 6.3*10^{-18}cm^{2}. Determine the mean free path of photons with energy of 20eV, for densities n_H = 1, 10 and 100 cm^{-3}. Compare this to mfp for photons with ionisation energy of hydrogen...