# Exercise 2.1-2

# Derive numbers for v0, vD, t, and l

| Show that the claims made in the backbone text are actually true (for room temperature = 300 K). Use the following equations taken from the backbone
|  | For the average velocity v0 of a particle zooming around in the crystal:
v0 | = | æ ç è | 3kT m | ö ÷ ø | 1/2
|  | For the mean time t between scattering:
t = | s · m n · e2
--- | ---
|  | For the drift velocity vD
vD | = – | E · e · t m
--- | --- | ---
|  | For the minimal mean free path length lmin obtained for vD = 0:
lmin = | 2 · v0 · t
--- | ---
| Of course, you need numbers for the concentration n of the free carriers and for the specific conductivity s
|  | Since we are essentially considering metals, you assume for a start that you have 1 free electron per atom if you want to find a number for n. Here are a few data needed for the calculation:
Atom | Density [kg · m–3] | Atomic weight × 1,66 · 10–27 kg | Conductivity s × 105 [W–1 · m–1] | Conzentration Atoms n [m–3] ???
--- | --- | --- | --- | ---
Na | 970 | 23 | 2.4 |
Cu | 8.920 | 64 | 5.9 |
Au | 19.300 | 197 | 4.5 |
| You may run into some trouble with the dimensions. Just look at conversions from, e.g. [eV] to [J], from W to V and A, and at the relations beween Volt, Ampere, Watts and Joule.

| Solution

With frame

2.1.2 Ohms Law and Classical Physics

Solution to Exercise 2.1-2

© H. Föll (Advanced Materials B, part 1 - script)