Answer
It takes 50 hours for a conduction electron to move 12 meters along the wire.
Work Step by Step
We can find the number $N$ of aluminum atoms per $m^3$:
$N = \frac{2.7~g/cm^3}{27~g/mol}$
$N = 0.1~mol/cm^3$
$N = (0.1~mol/cm^3)(6.02\times 10^{23}~atoms/mol)(10^6~cm^3/m^3)$
$N = 6.02\times 10^{28}~atoms/m^3$
We can find the number $n$ of conduction electrons per $m^3$:
$n = 3.5\times (6.02\times 10^{28})$
$n = 2.107\times 10^{29}$
We can write an expression for the drift speed:
$v_d = \frac{I}{n~q~A} = \frac{I}{n~q~\pi~r^2}$
$I$ is the current
$n$ is the number of conduction electrons per $m^3$
$q$ is the charge of one electron
$A$ is the cross-sectional area
$r$ is the cross-sectional radius
We can find the drift speed $v_d$:
$v_d = \frac{I}{n~q~\pi~r^2}$
$v_d = \frac{12~A}{(2.107\times 10^{29}~m^{-3})(1.6\times 10^{-19}~C)~(\pi)~(1.3\times 10^{-3}~m)^2}$
$v_d = 6.7\times 10^{-5}~m/s$
We can find the time it takes to move 12 meters along the wire:
$t = \frac{d}{v_d}$
$t = \frac{12~m}{6.7\times 10^{-5}~m/s}$
$t = (1.79\times 10^5~s)(\frac{1~h}{3600~s})$
$t = 50~h$
It takes 50 hours for a conduction electron to move 12 meters along the wire.
