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 magnesiums ions, m and n respectively, are

Options

A. `(1)/(2),(1)/(8)`
B. `1, (1)/(4)`
C. `(1)/(2),(1)/(2)`
D. `(1)/(4),(1)/(8)`

Explanation

To solve the problem, we need to determine the fractions \( m \) and \( n \) of octahedral and tetrahedral holes occupied by aluminum and magnesium ions, respectively, in a cubic close-packed (ccp) structure of oxygen atoms.

### Step-by-Step Solution:

1. **Identify the Number of Atoms and Holes**:
- In a cubic close-packed (ccp) structure, there are 4 oxygen atoms per unit cell.
- The number of octahedral holes in a ccp structure is equal to the number of atoms, which is 4.
- The number of tetrahedral holes is twice the number of octahedral holes, so there are \( 2 \times 4 = 8 \) tetrahedral holes.
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