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

Let the formula be `Mg_(x)Al_(y)O_(4) `
By inspection (or by solving `2x + 3y = 4 xx 2 ` ) : x = 1 , y = 2 `rArr " " MgAl_(2)O_(4)`
`rArr` For every 4 `O^(2-) ` lons there are `2Al^(3+)` ions and `1Mg^(2+)` ion.
and for every 4 `O^(2-)` ions there are 4 octahedral voids and 8 tetrahedral voids.
`rArr " m" = (2)/(4) = (1)/(2) and n = (1)/(8)`