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A metal oxide has the empirical formula M ₂ O ₃ . The oxide ions are arranged in a cubic close-packed (ccp) lattice. The metal ions M occupy:

Options

  1. A2 3 of the octahedral voids
  2. B1 3 of the octahedral voids
  3. C2 3 of the tetrahedral voids
  4. D1 2 of the octahedral voids

Correct answer

A. 2 3 of the octahedral voids

Step-by-step solution

In a cubic close-packed (ccp) lattice formed by oxide ions, the number of oxide ions per unit cell is 4 . Let the number of metal ions M per unit cell be x . From the empirical formula M ₂ O ₃ , the ratio of M to O is 2:3 . Therefore, x = 2 3 4 = 8 3 . In a ccp lattice with 4 atoms per unit cell, there are 4 octahedral voids and 8 tetrahedral voids. If the metal ions occupy octahedral voids, the fraction occupied is 8/3 4 = 2 3 . If the metal ions occupy tetrahedral voids, the fraction occupied is 8/3 8 = 1 3 . Com

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