# Drift Velocity, TCR, and Atomic/ Weight Percentages

1. Feb 10, 2008

### EugP

1. The problem statement, all variables and given/known data
I'm taking a metrials class, and there are 2 questions I'm not sure how to do. I would see the professor first, but he refuses helping students untill the assignments is submitted.

1) A circular tungsten (W) wire that is 0.1m long and 1mm in diameter has 9V dropped across it. Using a spreadsheet program such as Excel, generate a plot of the drift velocity as a function of temperature from 23C - 300C. Assume that density is temperature independent. Assume that W has 4 valence electrons per atom. Include in your plot, a write-up of the equations used.

2) What are the maximum atomic and weight percentages of Cu that can be added to Au without exceeding a resistivity that is twice that of pure gold? What are the maximum atomic and weight percentages of Au that can be added to pure Cu without exceeding twice the resistivity of pure copper?

2. Relevant equations
He never actually taught us any equations, just explained the theory, but this is what I found in the book:
1)
Drift Velocity
$$v _{dx} = \frac{e\tau}{m_e} E_x$$

Drift Mobility
$$\mu _d = \frac{\sigma}{en}$$

Conductivity
$$\sigma = en\mu _d$$

Number of atoms per unit volume
$$n = \frac{dN_A}{M_{at}}$$

3. The attempt at a solution
1) I don't know where to use the 9V in any of the equations. But just by using what I have, and some other equations I found online, I got:

$$n = \frac{dN_A}{M_{at}} = \frac{(19.25)(6.02 \times 10^{23})}{183.84} = 63.04 \times 10^{21}$$

$$\sigma = \frac{1}{\rho} = \frac{1}{AT} = \frac{1}{\pi (0.1cm)^2 T} = \frac{4}{\pi T}$$

$$\mu _d = \frac{\sigma}{en} = \frac{4}{\pi T (1.6\times 10^{-19})(63.04\times 10^{21})} = \frac{126.23\times 10^{-6}}{T}$$

At this point, I have no idea what to do, or whether what I've done is even correct so far. Please help.

2) For this problem, the only information I have is that the percentages must add up to 100, which is obvious. Any help here would be great.