# Mean free path calculation

1. Oct 28, 2009

### w3390

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

2. Oct 29, 2009

### willem2

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.

3. Oct 29, 2009

### 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.

4. Oct 29, 2009

### w3390

Nevermind...............figured it out