-->

The Solid State

Question
CBSEENCH12005506

The density of chromium is 7.2 g cm–3. If the unit cell is cubic with edge length of 289 pm, determine the type of the unit cell (Atomic mass of Cr = 52 amu).

Solution

Solution:
We have given that 

Gram atomic mass of Cr(M) = 52.0 g mol-1
   Edge length of unit cell (a) = 289 pm
   Density of unit cell (ρ) = 7.2 g cm-3
  
 Avogadro's Number (N0) = 6.022×1023 mol-1       

     ρ = Z×Ma3×NA×10-30

or              Z=ρ×a3×NA×10-30M
   
   Z=(7.2 g cm-3) × (289)3× (6.022×1023 mol-3) × (10-30 cm3)(52.0 g mol-1)=2

Since the unit cell has 2 atoms, it is body centre in nature.