# Resistivity mean free path and scattering time of copper

1. Mar 12, 2015

### SMC

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 that at room temperature copper has the electrical conductivity of 105 Ohm-1 cm-1 , and that its electron density is 1023 cm-3 and its Fermi velocity is 106 m/s.

so i know: mean free path = scattering time x velocity of electron
and velocity of electron can be approximated to fermi velocity

the question tells us: resistivity(room temp)/resistivity(T=0)=1000

resistivity in inversely proportional to scattering time so: scattering time(T=0)/scattering time(room temp)=1000

now my lecture notes say the typical value for scattering time in a metal (i assume at room temp.) is 10-14 seconds
so scattering time(T=0) is 1000 x 10-14=10-11 seconds right?

i also know from lecture notes that vf = \sqrt{\frac{2kTf}{m}} and typical value for fremi velocity in metals is 106 m/s. (k is Boltzmann constant and Tf is fermi temp. )

but how do i find the value of vf for low temp?

ps sorry i haven't used latex in a while so i'm not really sure why the expression for fermi velocity isn't showing correctly

Last edited: Mar 12, 2015
2. Mar 14, 2015

### Staff: Mentor

The fermi velocity is far above thermal velocities, it won't change significantly between absolute zero and room temperature.
I'm not sure if you are supposed to use this. That would ignore the copper-specific values for conductivity and electron density.