Question

A crystalline solid ab adopts sodium chloride type structure with edge length of unit cell as 745 pm and formula mass of 74.5

a.m.u.the density of 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

Answer 2

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