= Solution
One Pt(111) layer has height $d_{111}=a_0/\sqrt3=2.269\,\mathrm{\mathring A}$. In constant-height operation the separation above the island is therefore only $5.000-2.269=2.731\,\mathrm{\mathring A}$. With the same decay constant,
$$
\frac{I_{\rm island}}{I_{\rm terrace}}
=\exp(2q\,d_{111})
=\exp(5.446)\simeq232.
$$
Thus the ideal predicted current is \b[about $232\,\mathrm{nA}$]. This very large increase can exceed the useful current range or risk tip-surface contact; constant-height imaging is poorly suited to unexpected monolayer steps. Constant-current feedback can follow the height more safely, subject to its response bandwidth.
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