Question

A crystalline solid ab adopt sodium chloride type structure with age length of the unit cell as 7 45 pm and formula mass of 74.5 amu the density of the crystalline compound is

Answer 1

Given :
Edge of unit cell = a = 745pm=745 x 10⁻¹⁰ cm

Voulme of unit cell= a3 =(745)³x (10⁻¹⁰)³ cm³

mass of each unit cell = number of atoms in the unit cell x mass of each atom

=Zxm

mass of each atom =m= Atomic mass/ Avogadro number =M/No

Density of unit cell= mass of unit cell/ volume of unit cell

N₀=6.023 x10 ²³

Density of unit cell= ZxM/a3 x N₀

where Z= number of atoms =4
M=74.5 amu

Density = ρ =4x 74.5/ (6.022 x 10 ²³ ) x (745)³ x 10 ⁻³⁰
= 1.197 g/cm³

∴Density =1.197g/cm3

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