JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Solid State

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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

(A) $\frac{1}{2}, \frac{1}{8}$ ✓ Correct
(B) $1, \frac{1}{4}$
(C) $\frac{1}{2}, \frac{1}{2}$
(D) $\frac{1}{4}, \frac{1}{8}$

Answer: (A)

Solution

The mineral is spinel (

MgAl_{2} O_{4}

).

In ccp (fcc) structure:

Number of O atoms = 4 (per unit cell)
Octahedral holes = 4
Tetrahedral holes = 8

For

MgAl_{2} O_{4}

2 Al³⁺ ions occupy octahedral holes: fraction = 2/4 = 1/2
1 Mg²⁺ ion occupies tetrahedral hole: fraction = 1/8

Therefore, m = 1/2, n = 1/8, which is option (A).

JEE Advanced · 2015 · 24 May 2015 · Paper 1 · One or more correct options

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