2015 Jun 15: If I hammered and flattened a penny enough, could I cover the entire earth with it?

The answer to this question is kind of given. But the why is something that needs explaining and is something I do not have either the math nor the ability to explain. Chris, on the other hand, does. His explanations are in layperson terms and fun to read. So: “If I hammered and flattened a penny enough, could I cover the entire earth with it?”

Public Domain Image, source: NASA/JPL-Caltech.No. If you spread out the atoms from a single penny over the entire surface of the earth, you would no longer have a single piece of solid material since the atoms would be too far apart to bond to each other. Let’s do some careful calculations to show this result. A modern Unites States penny has a mass of 2.500 grams according to the US Mint. Since a penny is composed of 97.50% zinc and 2.50% copper, it therefore contains 2.4375 grams of zinc and 0.0625 grams of copper. At a molar mass of 65.380 grams per mole for zinc and 63.546 grams per mole for copper, a penny therefore contains 0.037282 moles of zinc and 0.00098354 moles of copper. Since a mole of atoms contains 6.0221 × 1023 atoms, there are 2.2452 × 1022 zinc atoms and 5.9230 × 1020 copper atoms in a penny, for a total of 2.3044 × 1022 atoms in a penny.

The earth has a surface area of 510,072,000 square kilometers, or 5.10072 × 1032 square nanometers. The surface area of the earth really depends on what you include in your definition of surface. For instance, if we wish to cover the area of every leaf on every tree and shrub with atoms from the penny, then this will change our answer. Surprisingly, it will not change our answer very much. Most of the earth is covered in relativity flat oceans, sandy deserts, snow fields, barren rocks, and meadows. Trees, shrubs, buildings, and other irregularly-shaped objects only cover a very small percentage of the earth (trees and buildings seem common to most of us humans because most of us live near crowded concentrations of trees and/or buildings). At any rate, we must pick some definition of earth’s surface area to make any calculations. The number cited above does not include the surface area of tree leaves and other small irregularities. In the context of trying to cover the earth with a flattened penny, you can think of this definition of surface area as us lowering a sheet of zinc so that it drapes along the tops of the trees, but does not wrap around any of the leaves or branches of the trees. The thinnest we could ever hammer a sheet of material is one atom thick. We therefore assume that we are creating a one-atom-thick planar sheet of material. Using the above value for earth’s surface area, we divide it by the number of atoms in a penny to find how much area each atom will occupy when the atoms are spread evenly across earth’s surface. We get the value of 2.21347 × 1010 square nanometers per atom, or 0.0000343 square inches per atom. This may seem like a small area, but it is huge compared to the types of areas spanned by simple molecules. ………………………………

The rest of the article can be found on Christopher Baird’s blog

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