Question

Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase: 970 kg m^-3. Are the two densities of the same order of magnitude? If so, why? 

Answer 1

Mass of 1 mole (N_A) of sodium atoms = 23 g.

Mass of 1 atom of sodium = 23g/N_A

= (23g x 10^-3 kg)/(6.022 x 10²³)

= 3.819 × 10^-26

Density of sodium atom = Mass/Volume

= ((3.819 x 10^-26)/(4/3)π x (2.5 x 10^-10)³

= 583.5 kg m^-3

≅ 0.6 × 10³ kg m^-3

970 kg m^-3 and 0.6 × 10³ kg m^-3

are of the same order of magnitude because atoms are tightly packed in solid-state, so the atomic mass density is quite close to the density of the solid.