A material has cubic close packed (ccp) array of oxide ions with 'm' fraction of octahedral holes occupied by aluminium ions and 'n' fraction of tetrahedral holes cocupied by magnesium ions to form a perfect crystal, 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`

Answer

A

Explanation

In ccp, each particle in close packing is associated with two tetrahedral voids and one octahedral void. Number of octahedral and tetrahedral holes is 4 and 8 respectively. From the balance of charge on the salt, we have `4O^(2-)` equivalent of -8 charge, which is balanced by `2Al^(3+)` and `1Mg^(2+)` or a charge of +8.
Therefore, the formula is `MgAl_(2)O_(4)`.
`therefore` Fraction of octahedral voids occupied by `Al^(3+)` ions=`(1)/(2)`
`therefore`Fraction of tetrahedral voids occupied by `Mg^(2+)` ions=`(1)/(8)`.