Chapter 4: Q49E (page 844)

Pure silicon at room temperature contains approximately $1.0 \times 10^{16}$ free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time for $τ$ 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

The mean time for $τ$ silicon at room temperature is $1.55 \times 10^{- 12} s$ .
Silicon has greater than the mean free for cooper.

Step by step solution

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 $τ$ .

$τ = \frac{m}{n e^{2} ρ}$

Where, is charge of the electron which is equal to $1.6 \times 10^{- 19} C$ , is the mass of electron which is equal to $9.11 \times 10^{- 31} kg$ , $n$ is concentration and $ρ$ is resistivity.

Determine the mean free time.

The resistivity $ρ$ of silicon is equal to $2300 Ω \cdot m$ and the

The mean free time for silicon is

$τ = \frac{m}{n e^{2} ρ} = \frac{9.11 \times 10^{- 31}}{(1.0 \times 10^{16}) (1.6 \times 10^{- 19}) (2300)} = 1.55 \times 10^{- 12} s$

From the expression $τ = \frac{m}{n e^{2} ρ}$ the mean free time is inversely proportional to concentration $n$ .

$τ \propto \frac{1}{n}$

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

Hence, mean free time $τ$ for silicon at room temperature is $1.55 \times 10^{- 12} s$ and silicon has greater than the mean free for cooper.

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Short Answer

Step by step solution

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

Determine the mean free time.

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