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 magnesiu

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

TestHub · Accepted Answer

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) $\frac{3}{2} + \frac{4}{8} = 2$ is correct.

(B) $3 \times 1 + 4 \times \frac{1}{4} = 4 \neq 2$ is incorrect.

(C) $3 \times \frac{1}{2} + 4 \times \frac{1}{2} = 4 \neq 2$ is incorrect

(D) $3 \times \frac{1}{4} + 4 \times \frac{1}{8} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \neq 2$ is incorrect.

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