13.14 Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms :

t

[Hint: Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few Å].

The volume of each atom=43πr3
The volume of N number of molecules=43πr3 N … (i)
The volume of one mole of a substance =Mρ … (ii) 
43πr3N=Mρ
r=3M4πρN3
For carbon: M = 12.01 ×10-3 kg,
ρ = 2.22 × 103 kgm3
r=3×12.01×10-34π×2.22×103×6.023×102313=1.29Å
Hence, the radius of a carbon atom is 1.29 Å.
For gold: M = 197.00 ×10-3 kg
ρ = 19.32 × 103kg m-3

r=3×197×10-34π×19.32×103×6.023×102313=1.59Å
Hence, the radius of a gold atom is 1.59 Å.
For liquid nitrogen:
M = 14.01 × 10-3kg
ρ = 1.00 × 103 kg m-3
r=3×14.01×10-34π×1.00×103×6.23×102313=1.77Å
Hence, the radius of a liquid nitrogen atom is 1.77 Å.
For lithium:
M = 6.94 × 10-3kg
ρ = 0.53 × 103kgm-3
r=3×6.94×10-34π×0.53×103×6.23×102313=1.73Å
Hence, the radius of a lithium atom is 1.73 Å.
For liquid fluorine:
M = 19.00 × 103 kg
ρ = 1.14 × 103kgm-3
r=3×19×10-34π×1.14×103×6.023×102313=1.88Å
Hence, the radius of a liquid fluorine atom is 1.88 Å.