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)`

Answer

A

Explanation

In ccp array:
Number of oxygen holes=4
Number of octahedral holes =4
Number of tetrahedral holes =8
Number of `Al^(3+)` ions=`4xxm`
Number of `Mg^(2+)` ions=`8xxm`
Molecule of mineral will be neutral , hence
`4(-2)+4m(+3)=8n(+2)=0`
`12m + 16 n=8`
`therefore m=(1)/(2) and n=(1)/(8)`