In a cubic closest packed structure of mixed oxides, the lattice is made up of oxide ions. Tetrahedral voids are occupied by divalent X2+ ions and octahedral voids are occupied by trivalent Y3+ ions.

Question

In a cubic closest packed structure of mixed oxides, the lattice is made up of oxide ions. Tetrahedral voids are occupied by divalent X2+ ions and octahedral voids are occupied by trivalent Y3+ ions. If only 50% of the octahedral voids are occupied, then the percentage of tetrahedral voids occupied is

Prashant Kotian · Accepted Answer

Correct answer: B. Let oxide ions be N (charge = -2N). Octahedral voids = N, occupied by Y3+ = 0.5N (charge = +1.5N). For charge neutrality, the positive charge of X2+ must be +2N - 1.5N = +0.5N. Thus, the number of X2+ ions is 0.5N / 2 = 0.25N. Total tetrahedral voids = 2N, so percentage occupied is (0.25N / 2N) × 100% = 12.5%.

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