Answer
$i_e = 1.0\times 10^{19}~electrons/s$
Work Step by Step
We can find the drift speed:
$v_d = \frac{e~\tau~E}{m}$
$v_d = \frac{(1.6\times 10^{-19}~C)(4.2\times 10^{-15}~s)(0.065~V/m)}{9.1\times 10^{-31}~kg}$
$v_d = 4.8\times 10^{-5}~m/s$
We can find the electron current:
$i_e = n_e~A~v_d$
$i_e = n_e~\pi~r^2~v_d$
$i_e = (8.5\times 10^{28}~electrons/m^3)~(\pi)~(0.90\times 10^{-3}~m)^2~(4.8\times 10^{-5}~m/s)$
$i_e = 1.0\times 10^{19}~electrons/s$
