Roughly how many atoms are in a 1 cm cube?

1 Answer
Jun 13, 2017

Answer:

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"#