Question

17. What is the mean time between collisions for electrons in (a) an aluminum wire and (b) an iron wire?

Short answer

(a) The mean time between collisions for electrons in an aluminum wire is $1.46\times {10}^{-14}\mathrm{s}$.

(b) The mean time between collisions for electrons in an iron wire is $4.18\times {10}^{-14}\mathrm{s}$.

Step-by-step solution

Given information Part (a)

The mean time between collisions for electrons in an aluminum wire.

Explanation Part (a)

The conductivity is given as $\sigma =\frac{n_e{e}^2\tau }{m}$
The mean time between collisions parametric as $\tau =\frac{m\sigma }{n_e{e}^2}$
In the case of aluminum, calculate to be,
$\tau =\frac{9.1\times {10}^{-31}\times 3.5\times {10}^7}{6.0\times {10}^{28}\times {\left(1.6\times {10}^{-19}\right)}^2}$

$=1.46\times {10}^{-14}\mathrm{s}.$

Final answer Part (a)

The mean time between collisions for electrons in an aluminum wire is $1.46\times {10}^{-14}\mathrm{s}$.

Given information Part (b)

The mean time between collisions for electrons in an iron wire.

Explanation Part (b)

The mean time of iron,
$\tau =\frac{9.1\times {10}^{-31}\times 1\times {10}^7}{8.5\times {10}^{28}\times {\left(1.6\times {10}^{-19}\right)}^2}$

$=4.18\times {10}^{-14}\mathrm{s}$

Final Answer Part(b)

The mean time between collisions for electrons in an iron wire is $4.18\times {10}^{-14}\mathrm{s}$.