Question 19.2: Drift Velocity of Electrons in Copper Assuming that all of t......
Drift Velocity of Electrons in Copper
Assuming that all of the valence electrons contribute to current flow, (a) calculate the mobility of an electron in copper and (b) calculate the average drift velocity for electrons in a 100 cm copper wire when 10 V are applied.
(a) The valence of copper is one; therefore, the number of valence electrons equals the number of copper atoms in the material. The lattice parameter of copper is 3.6151 × 10^{-8} cm and, since copper is FCC, there are four atoms/unit cell. From Table 19-1, the conductivity σ = 5.98 × 10^5 \ Ω^{-1} ⋅ cm^{-1}
n = \frac{(4 \ \text{atoms}/\text{cell})(1 \ \text{electron/atom})}{(3.6151 \ × \ 10^{-8} \text{cm})³/\text{cell}}= 8.466 \ × \ 10^{22} \ \text{electrons}/\text{cm}³
q = 1.6 × 10^{-19} \ C
μ=\frac{σ}{nq}=\frac{5.98 \ × \ 10^5 \ \Omega^{-1} ⋅ \text{cm}^{-1}}{(8.466 \ × \ 10^{22} \ \text{electrons}/\text{cm}^3)(1.6 \ × \ 10^{-19} \ C)}
=44.1 \ \frac{cm^2}{Ω ⋅ C}=44.1 \ \frac{cm^2}{V ⋅ s}
(b) The electric field is
E= \frac{V}{l}= \frac{10 \ V}{100 \ cm}=0.1 \ V/cmThe mobility is 44.1 cm²/(V ⋅ s); therefore,
\overline{v} = μE = [44.1 cm²/(V⋅s)](0.1 V/cm) = 4.41 cm/s
| Table 19-1 Electrical conductivity of selected materials at T = 300 K* | |||
| Material | Conductivity (ohm^{-1} · cm^{-1}) | Material | Conductivity (ohm^{-1} · cm^{-1}) |
| Superconductors | Semiconductors | ||
| Hg, Nb_{3}Sn | Group 4B elements | ||
| Yba_{2}Cu_{3}O_{7-x} | Infinite (under certain conditions | Si | 4 × 10^{-6} |
| MgB_{2} | such as low temperatures) | Ge | 0.02 |
| Metals | Compound semiconductors | ||
| Alkali metals | GaAs | 2.5 × 10^{-9} | |
| Na | 2.13 × 10^5 | AlAs | 0.1 |
| K | 1.64 × 10^5 | SiC | 10^{-10} |
| Alkali earth metals | Ionic Conductors | ||
| Mg | 2.25 × 10^5 | Indium tin oxide (ITO) | ∼10^{4} |
| Ca | 3.16 × 10^5 | Yttria-stabilized zirconia (YSZ) | <10^{14} |
| Group 3B metals | Insulators, Linear, and Nonlinear Dielectrics | ||
| Al | 3.77 × 10^5 | Polymers | |
| Ga | 0.66 × 10^5 | Polyethylene | 10^{-15} |
| Transition metals | Polytetrafluoroethylene | 10^{-18} | |
| Fe | 1.00 × 10^5 | Polystyrene | 10^{-17} to 10^{-19} |
| Ni | 1.46 × 10^5 | Epoxy | 10^{-12} to 10^{-17} |
| Group 1B metals | Ceramics | ||
| Cu | 5.98 × 10^5 | Alumina (Al_{2}O_{3}) | 10^{-14} |
| Ag | 6.80 × 10^5 | Silicate glasses | 10^{-17} |
| Au | 4.26 × 10^5 | Boron nitride (BN) | 10^{-13} |
| Barium titanate (BaTiO_{3}) | 10^{-14} | ||
| C (diamond) | <10^{-18} | ||