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
3kBT
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 mean free path length l obtained for vD = 0:
  l  =  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
[107 W–1 m–1]
Atomic density 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


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