Answer

According to the question the diameter of sodium is 2.5 Angstrom

= 2.5 x 10^-10 m

Therefore, the radius will be half of the above value, i.e., 1.25 x 10^-10 m

Expression for the volume of sodium atom is

V= (4/3)πr³

Putting values and solving

= (4/3) x (22/7) x (1.25 x 10^-10) ³

V = 8.177 x 10^-30 m³

Mass of 1 mole atom of sodium = 23 g

M = 23 x 10^-3 kg

We know that the 1 mole of sodium contains 6.023 x 10²³ atoms

Therefore, the mass of one sodium atom will be given by –

M= 23 x 10^-3/6.023 x 10²³

M = 3.818 x 10^-26 kg

We know that the expression for atomic mass density of sodium is

ρ = M/V =3.818 x 10^-26/8.177 x 10^-30

ρ = 0.46692 x 10⁴= 4669.2 kg m^-3

Therefore, 4669.2  kg m^-3 is the density of sodium in its solid state but in the crystalline phase its density is 970 kg m^-3.

As a result, they are in a different order. Atoms are tightly packed in the solid state, but in the crystalline state, they organize themselves in a void-filled sequence. As a result, the density of the solid phase is larger than that of the crystalline phase.