Pure silicon at room temperature contains approximately1.0×1016 free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time forτ silicon at room temperature. (b) Your answer in part (a) is much greater than the mean free time for copper given in Example 25.11. Why, then, does pure silicon have such a high resistivity compared to copper?

Short Answer

Expert verified
  1. The mean time forτ silicon at room temperature is 1.55×10-12s.
  2. Silicon has greater than the mean free for cooper.

Step by step solution

01

Define the ohm’s law, resistance (R) and power (P).

The average time between the collisions for the electron is known as mean free time τ.

τ=mne2ρ

Where, is charge of the electron which is equal to 1.6×10-19C, is the mass of electron which is equal to 9.11×10-31kg,n is concentration andρ is resistivity.

02

Determine the mean free time.

The resistivity ρof silicon is equal to 2300Ω·mand the

The mean free time for silicon is

τ=mne2ρ=9.11×10-311.0×10161.6×10-192300=1.55×10-12s

From the expressionτ=mne2ρ the mean free time is inversely proportional to concentration n.

τ1n

As the silicon has less valuen than the copper. So, silicon has larger value.

Hence, mean free timeτ for silicon at room temperature is1.55×10-12s and silicon has greater than the mean free for cooper.

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