Roughly how many atoms are in a 1 cm cube?

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Answer 1 · 2017-06-13T15:42:59

There are about $10^24$ atoms in a 1 cm cube.

Since we are making only a crude approximation, let's assume that the atom fits a cube that is $10^"-10" color(white)(l)"m"$ on edge.

In centimetres, the length $l$ of an edge is

$l = 10^"-10" color(red)(cancel(color(black)("m"))) × "100 cm"/(1 color(red)(cancel(color(black)("m")))) = 10^"-8" color(white)(l)"cm"$

The volume $V$ of this little cube (1 atom) is

$V = l^3 = (10^"-8"color(white)(l) "cm")^3 = 10^"-24"color(white)(l) "cm"^3$

The number of atoms in $"1 cm"^3$ is then

$1 color(red)(cancel(color(black)("cm"^3))) × "1 atom"/(10^"-24" color(red)(cancel(color(black)("cm"^3)))) = 10^24color(white)(l) "atoms"$