Calculate the volume of wire that would contain 6e18 free electrons, assuming 1 electron per atom.

You can intuit it by knowing Avogadro's constant is 6e23.

So 1e-5 mol, 1 mol of (atomic) Copper is 63g, so that's 6e-4g of copper. Density of copper is 9g/cm3 so let's say 1e-4 cm3 = 1e-1 mm3 = 0.1 cubic mm of copper.

So one amp in a copper wire is equivalent to 0.1 cubic mm of that wire's electrons flowing out each second. I'd say that's "barely moving".

(very roughly)