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15 February, 10:19

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?

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Answers (1)
  1. 15 February, 12:59
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    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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