Relaxation time = displacement lifetime of fermi sphere?

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SUMMARY

The discussion centers on the relationship between relaxation time (\tau) and the lifetime of Fermi sphere displacement in the context of electron behavior under an applied electric field. The user seeks clarification on whether these two concepts are equivalent or distinct, as both are denoted by \tau in their notes. Key equations provided include electrical conductivity (\sigma = \frac{n e^2 \tau}{m}) and electrical resistivity (\rho = \frac{1}{\sigma}=\frac{m}{n e^2 \tau}). The user also mentions specific data for copper, including a relaxation time of 2.50e10-14s, density of 8940 kg/m³, and molar mass of 63.5 g.

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  • Understanding of Fermi sphere concepts in solid-state physics
  • Familiarity with electrical conductivity and resistivity equations
  • Knowledge of electron dynamics in electric fields
  • Basic principles of solid-state physics and material properties
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  • Study the derivation and implications of the electrical conductivity equation
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Homework Statement



I just want to clear this up, I am a little confused:

when an electric field is applied there is a force on the electron K-states thus displacing the fermi surface/sphere

Is the relaxation time (\tau)= lifetime of fermi sphere displacement

or is lifetime of displacement= reciprocal relaxation time

both are labebel as \tau in my notes and related as below but how can they be the same?


Homework Equations



\sigma = \frac{n e^2 \tau}{m} electrical conductivity

\rho = \frac{1}{\sigma}=\frac{m}{n e^2 \tau} electrical resistivity
 
Last edited:
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Given the following data on copper, how do i calculate the resistivity?

Relaxation time: 2.50e10-14s
Density: 8940Kgm-3
molar mass: 63.5g

is there an equation for it.
 

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