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

The correct answer is (A)

In ccp, O2– ions are 4.
Hence total negative charge = –8
Let Al³⁺ ions be x, and Mg²⁺ ions be y.
Total positive charge = 3x + 2y

⇒ 3x + 2y = 8
This relation is satisfied only by x = 2 and y = 1.
Hence number of Al³⁺ = 2.
and number of Mg²⁺ = 1.
⇒n = fraction of octahedral holes occupied byAl3+ =2/4=1/2

and m = fraction of tetrahedral holes occupied by Mg²⁺ =1/8

Hence, answer is (A)