Answer
$t = 2.6~\times 10^5~s$
Work Step by Step
We can find the electron current:
$i_e = n_e~A~v_d$
$i_e = n_e~\pi~r^2~v_d$
$i_e = (5.90\times 10^{28}~electrons/m^3)~(\pi)~(0.50\times 10^{-3}~m)^2~(5.0\times 10^{-5}~m/s)$
$i_e = 2.317\times 10^{18}~electrons/s$
We can find the time it takes one mole of electrons to flow through a cross-section:
$t = \frac{6.02\times 10^{23}~electrons}{2.317\times 10^{18}~electrons/s}$
$t = 2.6~\times 10^5~s$
