Exercise 2.1-2

Derive numbers for v₀, v_D, 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)