What is Mean free path: Definition and 60 Discussions
In physics, mean free path is an average distance over which a moving particle (such as an atom, a molecule, a photon) substantially changes its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles.
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...
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.
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...
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
A supernova can produce a neutron star with typical radius 10km. Assume the neutron star matter consists of iron nuclei (A=56), produced by the electron capture reaction:
e^{-}+Co\rightarrowFe+\nu_{e}
The matter density is \rho=10^{5} tonne mm^{-3} and the neutrino...
Homework Statement
I'm off by a factor of 106 and I have no idea why.
"Silver has a density of 10.5*103 kg/m3 and a resistivity of 1.60*10-8 Ω*m at room temperature. Assume that each silver atom contributes one electron to the electron gas. Assume that EF = 5.48 eV"
What's the mean free...
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)?
Hello all,
I'm modeling a situation in which a gas moves through a pressure gradient established by a quartz frit with 40-100 μm sized pores. What I'm interested in finding out is how the mean free path of the gas changes after it exits the frit region, if at all.
I think that the mean...
Homework Statement
obtain an expression for the thermal conductivity of a gas at ordinary pressures. The thermal conductivity of Argon (atomic weight 40) at STP (standard temp and pressure) is 1.6e-2 W/mK. Use this to calculate the mean free path in Argon at STP. Express the mean free path...
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?
I am investigating the microwave (say, 28 GHz to 30 GHz) reflection properties of a thin (say, 35 nm) film of aluminum that is being used to plate a graphite reflector antenna. I found a useful paper (R. C. Hansen and W. T. Pawlewicz, ``Effective conductivity and microwave reflectivity of thin...
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?
Let's assume we have an ideal gas made up of rod-like (i.e., cylindrical) particles, which have a length (L) 100 times their width or diameter (d).
Clausius's equation for calculating mean free path is based on spherical particles. The ratio of mean free path to particle radius exists in the...
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
Estimate the mean free path of an electron in mercury vapour at a temperature of 160 degrees C, where the vapour pressure is 11.28 mmHg
It gives the standard atmospheric pressure as 761.84 mmHg.
Homework Equations
Mean free path= (Boltzmann's constant times...
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...