# Roughly how many atoms are in a 1 cm cube?

Jun 13, 2017

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

#### Explanation:

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

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

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

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 ${\text{1 cm}}^{3}$ 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"