If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of…

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
  1. 12,18
  2. 1,14
  3. 12,12
  4. 14,18

Solution

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 by Al3+
=24=12
and m = fraction of tetrahedral holes occupied by Mg2+
=18

Asked in: JEE Advanced 2015 (Paper 1)

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