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In class we're talking about a scanning tunnelling microscopy.

In the example a sharp metallic tip is held just above a conducting surface with a voltage between the tip and the surface with a current flowing. How would the current vary with the separation between tip and sample (just the functional variation)? If the energy of an electron in the conductors is 5V lower than the energy of the electron in a vacuum, what is the characteristic length scale over which the current will be measurable?

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