Resistivity, ρ = m/ne²τ, where m is electron mass, n is the current carrier (electron) density, e is electron charge magnitude, and τ is the mean time between collisions.

n = 2.5 × 10¹³electrons/cm³ × (100cm/1m)³ = 2.5 × 10¹⁹ electrons/m³

Solving for τ:

τ = m/ne²ρ = (9.11 × 10^-31 kg)/((2.54 × 10¹⁹ electrons/m³)(1.602 × 10^-19 electrons)²(0.60 Ω•m)) = 2.33 × 10^-12 s

The mean free time for germanium at 20°C is 2.33 × 10^-12 s

1/τ = 4.29 × 10¹¹ collisions/s is the number of collisions an electron makes in one second.

b)

The mean free time for copper is about 2.4 × 10^-14 s at room temperature.

Resistivity heavily depends on charge carriers' concentration, rather than mean free time.

The concentration of charge carriers in copper is 8.5 × 10²⁸ free electrons/m³

The high resistivity is linked to a low concentration of available charge carriers.

Microscopic View of Current Practice Problems