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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?

Respuesta :

meerkat18
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. 

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