Question

Roughly how many atoms are in a 1 cm cube?

Answer 1

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^"-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"`