Question

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are 

(A) 1/2 , 1/8

(B) 1 , 1/4

(C) 1/2 , 1/2

(D) 1/4 , 1/8

Answer 1

Correct option is (A) 1/2 , 1/8

In ccp lattice: 

Number of O atoms → 4 

Number of Octahedral voids → 4 

Number of tatrahedral voids → 8 

Number of Al³⁺ = 4 x m

Number of Mg²⁺ = 8 x n

Due to charge neutrality

4 (-2) + 4m (+3) + 8n (+2) = 0

∴ m = 1/2 and n = 1/8