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 mass 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

Given: The size of sodium atom is 2.5  A o and its density in crystalline phase is 970 kg  m −3 .

The radius of the sodium atom is,

r= 1 2 ×2.5  A o =1.25  A o =1.25× 10 −10  m

The volume of the sodium atom is given as,

V= 4 3 π r 3

By substituting the values in the above equation, we get

V= 4 3 ×3.14× ( 1.25× 10 −10 ) 3 =8.177× 10 −30   m 3

By Avogadro Hypothesis, one mole of sodium contains 6.023× 10 23 atoms and has mass of 23× 10 −3  kg.Therefore mass of 1 atom is,

m= 23× 10 −3 6.023× 10 23 =3.819× 10 −26  kg

The density of sodium atom is given as,

ρ= m V

By substituting the values in the above equation, we get

ρ= 3.819× 10 −26 8.177× 10 −30 =4.67× 10 −3   kg/m 3

Thus, the density of sodium atom is 4.67× 10 −3   kg/m 3 .

The density of sodium atom and density of sodium in its crystalline phase are not in the same order. This difference in density is due to that in crystalline phase, the inter-atomic separation is very small as they are closely packed.