= Solution
The pressure is $10^{-8}\,\mathrm{mbar}=10^{-6}\,\mathrm{Pa}$. The molecular arrival flux from an ideal gas is
$$
J=\frac{P}{\sqrt{2\pi m k_BT}}.
$$
Because the residual-gas composition, temperature and sticking probability are not specified, the answer is an \b[order-of-magnitude monolayer-equivalent exposure time], not a unique coverage prediction. Take $T=300\,\mathrm K$, a nitrogen-like molecular mass $m=28u=4.65\times10^{-26}\,\mathrm{kg}$, and unit sticking probability. Then
$$
J\simeq2.88\times10^{16}\,\mathrm{m^{-2}\,s^{-1}}.
$$
Use the given $0.5\,\mathrm{nm}$ molecular-layer scale as an approximate intermolecular spacing, giving $N_s\sim(0.5\,\mathrm{nm})^{-2}=4\times10^{18}\,\mathrm{m^{-2}}$. Thus
$$
\boxed{\tau_{\rm ML}\sim\frac{N_s}{sJ}\simeq\frac{1.4\times10^2}{s}\,\mathrm s.}
$$
For $s=1$, this is \b[a few minutes]; assuming instead $10^{19}\,\mathrm{m^{-2}}$ sites gives about $350\,\mathrm s$, the same rough scale. A clean-looking vacuum pressure does not imply a contamination-free surface. Desorption and a small sticking probability can greatly lengthen net accumulation, while residual water or hydrocarbons can dominate the chemistry. Full saturation in a site-blocking adsorption model is not exactly the same as one monolayer-equivalent incident fluence.
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