The fraction of octahedral voids filled by `Al^(3+)` ion in `Al_(2)O_(3)(r_(Al^(3o+))//r_(O^(2-)) = 0.43)` is

Options

A. `0.43`
B. `0.287`
C. `0.667`
D. `1`

Answer

C

Explanation

`Al_(2)O_(3)` is a corundum-type structure in `Al_(2)O_(3)`, anion `(O^(2-))` forms fcc arrangement.
`:.` Number of `O^(2-) = 4` (corner `+` face centre `= 1 + 3 = 4`)
`:.` Number of `OVs = 4`.
Cation `Al^(3+)` are present ` = (2)/(3) cc OV_(s) = (2)/(3) xx 4 = (8)/(3)`
Hence, fraction of OVs filled by `Al^(3+)` ion `= ((2)/(3) xx 4)/(4)`
`= 0.667`