Question

Hcp crystal in made of a ions and b ions are arranged in 2/3rd of octahedral voids the simplest formula of unit cell is

Answer 1

No. of a ions = 6 
no. of octahedral voids = 6 
no. of b ions  =  (2/3)x 6 = 4 

hence , simplest formula
a : b = 6 : 4 = 3 : 2 
a₃b₂
so , you got that answer

Answer 2

Hcp crystal in made of a ions and b ions are arranged in 2/3rd of octahedral voids.

We know that the packing fraction of both face centered cubic and hexagonal close packed structures is 0.74, consist of closely packed planes of atoms, and have coordination number of 12.

Total no of atoms in Hcp crystal is 4

8 atoms are in the corner and 6 atoms are in the face.

No of octahedral voids=4

Nof of b ions are=4*2/3=8/3

No of a ions are 4

Simplest formula is a4b8/3 that is a12b8