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Q & A: Amount of gold required to paint the Moon?

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Most recent answer: 12/12/2015
Q:
Amount of gold required to paint (one atomic thickness) whole moon.
- Dr.Madhav Pakhare (age 54)
Kabul,Afghanistan
A:

Let us first estimate the number of atoms (n) that is required to tile the whole 2D spherical surface of the Moon. Obviously, we can neglect the curvature of the lunar surface, since there is about 16 orders of magnitude difference between the lunar diameter (R=1738km) and the atomic radius of gold (Au, r=67pm). So, we need to pack spherical objects with surface cross-section πr^2 side by side to cover an area 4πR^2. then you roughly need n=4R^2/r^2 = 10^33 atoms or about 10^9 moles of gold. Note that there is a close packing problem of spheres, which I simply ignored in this rough estimations: spheres can cover at most 74% percent of a 2D flat surface.

Since gold has molecular weight 79g/mol, this would correspond to more than 10^4 tonnes of gold, which is somewhat more than the combined gold reserves of USA and Germany. So surprisingly, there is enough gold on Earth to cover the Moon's surface in principle.

Tunc


(published on 12/12/2015)

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