Answer
$2.07\times 10^{-19}$ $s$
Work Step by Step
If the beam consisted of electrons rather than protons, the value of $b$ becomes
$b=\sqrt {\frac{8\times\pi^2\times 9.1\times 10^{-31}\times(6-5)\times1.6\times 10^{-19}}{(6.63\times 10^{-34})^2}}$
or, $b\approx 5.114\times 10^{9}$ $m^{-1}$
The (dimensionless) quantity $2bL$ is then
$2bL=2\times (5.114\times 10^{9})\times (7\times 10^{-10})\approx 7.1596$
and, the transmission coefficient is
$T\approx e^{-2bL}= e^{-7.1596}=7.7436\times 10^{-4}$
Thus, we get the waiting time for one electrion to be transmitted
$t=\frac{1}{6.25\times 10^{21}\times 7.7436\times 10^{-4}}$ $s$
or, $t=2.07\times 10^{-19}$ $s$
Therefore, we have to wait $2.07\times 10^{-19}$ $s$ for one electron to be transmitted.
