A substance's density is defined as its mass per unit volume. The density symbol that is most commonly used is \rho
\text{ Density }=\frac{\text{ mass }}{\text{ volume }}
Given that
Sodium atom average density \rho = ?
Size(Diameter) of the sodium atom D = 2.5 A^{^0}
Avogadro's number NA = 6.023 * 10^{23} atoms
Atomic mass of sodium = 23 g = 23* 10^{-3} kg
Density of the sodium in its crystalline state \rho_c= 970 kg m^3
Step 1: Calculating the volume of the sodium atom
Radius of the Sodium atom r = \frac{D}{2} = \frac{2.5}{2} = 1.25 A^{^0}
r = 1.25 * 10^{-10} m \because \text{1 angstrom = } 10^{-10}
Volume sodium atom (sphere) = \frac{4}{3}\pi r^3
= \frac{4}{3}* 3.14 * (1.25 * 10^{-10})^3
= 8.1845 * 10^{-30} m^3
Step 2: Mass of the sodium atom using the Avogadro's law
1 mole of the sodium contains 6.023 * 10^{23} atoms has a mass 23* 10^{-3} kg
Mass of one sodium atom = ?
Mass of sodium atom = \frac{23* 10^{-3}}{6.023 * 10^{23}}
= 3.818 * 10^{-26} kg
Step 3: Determine the sodium atom average density
\text{ sodium atom average density } = \frac{\text{ Mass of sodium atom }}{\text{ Volume sodium atom }}
= \frac{3.818 * 10^{-26}}{ 8.1845 * 10^{-30}}
=4.67*10^3\ \ kg/m^3
Solid sodium atom average density \rho_s=4.67*10^{\ 3\ }\ \ kg/m^3
Given that, \rho_c= 970 kg m^3
Thus, in its crystalline form, the density of sodium and the density of solid sodium are not the same. Since atoms are packed tightly during the solid process. In the crystalline phase, therefore, the interatomic separation is very small.