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Atomic Spacing

The density of copper is 8.9 x 10³ kg/m³. Each copper atom has a mass of 63u, according to the periodic table. One u is an atomic mass unit, equal to 1.66 x 10^-27 kg. Use this information to find the average spacing between copper atoms:

Solution:

Since one copper atom has a mass of 63u x 1.66 x 10^-27 kg/u = 1.04 x 10^-25 kg, we can calculate how many atoms there are in a cubic meter:

N = (8.9 x 10³ kg/m³)/(1.04 x 10^-25 kg/atom) = 8.5 x 10²⁸ atoms/m³.

Consider this to be a cubical arrangement of n x n x n copper atoms, where n is the number on one edge of the cube. The number n is then N^1/3 = 4.4 x 10⁹ atoms. If there are n atoms in a meter, then the distance between atoms is 1/n = 2.3 x 10^-10 m.

The spacing between copper atoms is about 2.3 x 10^-10 m, or 0.23 nm. Duplicate this calculation for iron ( r = 7800 kg/m³, m = 56u); water (r = 1000 kg/m³, m = 18u), and helium (r = 0.179 kg/m³, m = 4u). Comment on the differences between solids, liquids, and gases.