Mean free path at low temperatures

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SUMMARY

The discussion focuses on calculating the mean free path of electrons and phonons in metals at low temperatures. The formula for mean free path is given as l = (σn)^(-1), where l represents the mean free path, n is the number of target particles per unit volume, and σ is the effective cross-sectional area for collision. Additionally, the concept of 'attenuation length' is introduced as a related measure in particle physics. The inquiry also raises the question of whether different mean free paths exist near and far from walls.

PREREQUISITES
  • Understanding of mean free path in physics
  • Familiarity with thermal resistance concepts
  • Knowledge of particle density and collision cross-section
  • Basic principles of electron and phonon behavior in metals
NEXT STEPS
  • Research the calculation of mean free path for electrons in metals
  • Explore phonon transport mechanisms in low-temperature physics
  • Study the concept of attenuation length in particle physics
  • Investigate the effects of boundary conditions on mean free path
USEFUL FOR

Students and researchers in physics, particularly those focusing on thermal properties of materials, as well as anyone interested in the behavior of electrons and phonons in low-temperature environments.

Armandito
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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 anybody tell me where I could find that?

By the way, Is there two different mean free path : far from the wall and near the wall?

Best thanks!

Homework Equations





The Attempt at a Solution

 
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Armandito said:

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 anybody tell me where I could find that?

By the way, Is there two different mean free path : far from the wall and near the wall?

Best thanks!

Homework Equations





The Attempt at a Solution


I assume that you know what mean free path is so here is the basic formula for the mean free path:

[tex]l=\left(\sigma n\right)^{-1}[/tex]

where [tex]l[/tex] is the mean free path, [tex]n[/tex] is the number of target particles per unit volume, and [tex]\sigma[/tex] is the effective cross sectional area for collision.

From this I guess you can derive whatever you want to get about mean free path.

If you are doing the particle physics, then the mean free path is replaced by the similar concept called 'attenuation length' or 'absorption length.' It is the distance [tex]\lambda[/tex] into a material when the probability (that particle has not been absorbed) has dropped to [tex]1/e[/tex].

Hope it helped.
 

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