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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

Options

  1. A1 2 , 1 8
  2. B1 , 1 4
  3. C1 2 , 1 2
  4. D1 4 , 1 8

Correct answer

A. 1 2 , 1 8

Step-by-step solution

No. of oxygen atoms per unit cell in ccp = 4 O 2 - No. of octahedral voids per unit cell = 4 A l 3 + No. of Tetrahedral voids per unit cell = 8 M g 3 + Total negative charge due to oxygen atoms = 8 Net charge must be zero. m4 3 + 2n 8 + 4 - 2 = 0 3 m + 4 n = 2 (A) 3 2 + 4 8 = 2 is correct. (B) 3 × 1 + 4 × 1 4 = 4 ≠ 2 is incorrect. (C) 3 × 1 2 + 4 × 1 2 = 4 ≠ 2 is incorrect (D) 3 × 1 4 + 4 × 1 8 = 3 4 + 2 4 = 5 4 ≠ 2 is incorrect.

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