Pure silicon contains approximately 1.0 X 1016 free electrons per cubic meter. (

a. Referring to Table 25.1, calculate the mean free time., for silicon at room temperature. (

b. Your answer in part (

a. is much greater than the mean free time for copper given in Example 25.12. Why, then, does pure silicon have such a high resistivity compared to copper?

A. The formula for mean free time is:

t = V / (4π√2 r²vN)

where

N = 1*10¹⁶ molecules (per m³)

V = 1 m³

r = 111*10⁻⁷m (atomic radius of silicon)

Let's solve for v first:

v = √ (3RT/M) = √ (3 (8.314 m³·Pa/mol·K) (25 + 273 K) / 28.1 g/mol Si)

v = 16.26 m/s

t = (1 m³) / (4π√2 (111*10⁻⁷m) ² (16.26 m/s) (1*10¹⁶ molecules))

t = 2.81*10⁻9 s

Pure silicon has a high resistivity relative to copper because copper is a conductor, while silicon is a semi-conductor.