Q27 of 39 Page 35

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?

Given,


Diameter of the sodium atom, (d)= 2.5 Å


∴ Radius, (r) = 1.25 Å


Density of sodium in crystalline phase, (ρc)= 970 kg m-3


Consider every atom of sodium to be sphere,


Volume (V) = r3 m3


∴ V = ×3.14× (1.25×10-10)3 m3


≈ 8.18×10-30 m3


We know that,


According to Avogadro law, a mole contains 6.023×1023 atoms.


The molecular weight of sodium atom, (M) = 23 g = 23×10-3 kg


Density, (ρ) = kg/m3


∴ ρ = ≈ 4.67×10-7 kg/m3


Thus,


The density of sodium in crystalline phase (ρc) is much higher than the density of general sodium in general configuration (ρ). Because, sodium atoms in crystalline phase have very less inter-atomic separation.


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