(A) Using the data and results from Example 27.1 and the classical model of electron conduction, estimate the average time interval between collisions for electrons in household copper wiring.

(B) Assuming that the average speed for free electrons in copper is $1.6 \times 10^{6}$ m/s and using the result from part (A), calculate the mean free path for electrons in copper.

Question

(A) Using the data and results from Example 27.1 and the classical model of electron conduction, estimate the average time interval between collisions for electrons in household copper wiring.

(B) Assuming that the average speed for free electrons in copper is [latex] 1.6 imes 10^{6} [/latex] m/s and using the result from part (A), calculate the mean free path for electrons in copper.

Accepted Answer

From Equation 27.17, we see that

[latex] ho=\frac{1}{\sigma}=\frac{m_{e}}{n q^{2} au} [/latex] (27.17).

[latex] au=\frac{m_{e}}{n q^{2} ho} [/latex].

[latex] ext { where } ho=1.7 imes 10^{-8} \Omega \cdot m ext { for copper and the carrier } [/latex] density is [latex] n=8.49 imes 10^{28} ext { electrons } / m ^{3} [/latex] for the wire described in Example 27.1. Substitution of these values into the expression above gives

[latex] au=\frac{9.11 imes 10^{-31} kg }{\left(8.49 imes 10^{28} m ^{-3} ight)\left(1.6 imes 10^{-19} C ight)^{2}\left(1.7 imes 10^{-8} \Omega \cdot m ight)} [/latex].

[latex] =2.5 imes 10^{-14} s [/latex].

(B) Assuming that the average speed for free electrons in copper is [latex] 1.6 imes 10^{6} [/latex] m/s and using the result from part (A), calculate the mean free path for electrons in copper.

From Equation 27.18,

[latex] au=\frac{\ell}{\bar{v}} [/latex] (27.18).

[latex] \ell=\bar{v} au=\left(1.6 imes 10^{6} m / s ight)\left(2.5 imes 10^{-14} s ight) [/latex].

[latex] =4.0 imes 10^{-8} m [/latex].

which is equivalent to 40 nm (compared with atomic spacings of about 0.2 nm). Thus, although the time interval between collisions is very short, an electron in the wire travels about 200 atomic spacings between collisions.

Question 27.5: (A) Using the data and results from Example 27.1 and the cla...

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