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

For ccp arrangment , `Z = 4`
`:.` No. of O atoms = 4
No. of octahedral voids = 4
No. of tetrahedral voids = `4 xx 2 = 8`
No. of `Al^(3+)`ions = `m xx 4`
No. of `Mg^(2+)` ions = `n xx 8`
Thus the formula of mineral is
`Al_(4m) Mg_(8n) O_(4)`
`4m (+3) + 8n(+2) + 4(-2) = 0`
`12 m + 16 n - 8 = 0`
`4(3m + 4n - 2) = 0`
`:. " " 3m + 4n = 2`
Possible values of m and n are
`3 xx 1/2 + 4 xx 1/8 = 2 " "` true
`3 xx 1 + 4 xx 1/4 = 2 " "` not true
`3 xx 1/2 + 4 xx 1/2 = 2" "` not true
`3 xx 1/4 + 4 xx 1/8 = 2 " " ` not true.