What is the mean free path of conduction electrons in Na at T = 273 K?

[w3390]

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 Equations

The Attempt at a Solution

I think the equation I should be using is \rho=(Me)(Vav)/(Ne)(e)^2\lambda. The main issue with this problem is that the units are all over the place. Using this equation, I get \lambda= 3.56nm for Na. All I'm concerned with right now is Na. I have a feeling though that since I am given the Fermi speed, I need to use a formula that incorporates the Fermi speed, but I cannot find any that seem relevant.

 

[willem2]

I think the equation I should be using is \rho=(Me)(Vav)/(Ne)(e)^2\lambda.

What is V_av in this equation?
The units of this equation are correct. The unit of Ne is m^-3, The units of e is As.

 

[w3390]

Vav in this equation is sqrt(3kT/Me), where k= 1.38e-23 J/K. This is where I think the problem lies. Using the equation I stated in my first post, there is no place to substitute the Fermi speeds. I cannot find any equation that fits the Fermi speed to the resistivity. Since I am given the Fermi speed, I know how to find the Fermi energy, but that gets me nowhere.

 

[w3390]

Nevermind...figured it out