Answer
aluminum: $\tau = 2.1\times 10^{-14}~s$
iron: $\tau = 4.2\times 10^{-15}~s$
Work Step by Step
We can find the mean time between collisions for electrons in an aluminum wire:
$\sigma = \frac{n_e~e^2~\tau}{m}$
$\tau = \frac{\sigma~m}{n_e~e^2}$
$\tau = \frac{(3.5\times 10^7~S/m)(9.1\times 10^{-31}~kg)}{(6.0\times 10^{28}~m^{-3})(1.6\times 10^{-19}~C)^2}$
$\tau = 2.1\times 10^{-14}~s$
We can find the mean time between collisions for electrons in an iron wire:
$\sigma = \frac{n_e~e^2~\tau}{m}$
$\tau = \frac{\sigma~m}{n_e~e^2}$
$\tau = \frac{(1.0\times 10^7~S/m)(9.1\times 10^{-31}~kg)}{(8.5\times 10^{28}~m^{-3})(1.6\times 10^{-19}~C)^2}$
$\tau = 4.2\times 10^{-15}~s$
