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12:08pm on Sunday, 27th April, 2014:

Weird

From the *New York Times International Weekly*, which is a pull-out for *The Observer*:

So 28 grams of graphene could cover 28 football fields. Why not say that 1 gram of it could cover 1 football field? Or 142,857 grams of it could cover 142,857 football fields?

Well, basically one ounce is about 28 grams, so this article converted the ounce into grams for its international audience. The person who did the conversion didn't notice the cancellation (or did but was forbidden from making it for some reason). Journalists aren't renowned for their arithmetic skills.

Hmm. Carbon has an atomic weight of 12.0107, so treating the carbon atoms that make up graphene individually (which may or may not make sense), a mole of carbon weighs 12.0107g. There are 6.022 x 10^{23} atoms in a mole. A gram of carbon therefore has (6.022 x 10^{23})/12.0107 = 5.01386264 x 10^{22} atoms in it.

The separation of atoms in graphene is the same as in a layer of graphite: 0.142nm, or 1.42 x 10^{-10}m. They're laid out in a lattice hexagonally. The number of hexagons is half the number of atoms (because a hexagon has 6 sides and each corner (atom) is part of 3 hexagons), so 5.01386264 x10^{22} atoms means 2.50693132 x 10^{22} hexagons. The area of a hexagon with a side length L is (3 x 3^{½} x L^{2})/2. Therefore the area of 2.50693132 x10^{22} hexagons with a side length of 1.42 x 10^{-10}m is (2.50693132 x 10^{22} x 3 x 3^{½} x (1.42 x 10^{-10})^{2})/2 square metres.

So that's about 1313.32137 square metres give or take some rounding errors. This is about the same as a square with sides just over 36m long.

Hmm, seems a bit small for a football field. I wonder where I made my mistake?

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