Question

If the length of the body diagonal of a FCC unit cell is xÅ, the distance between two octahedral voids in the cell in Å is ______.

Options

• `x/sqrt2`

• `x/sqrt3`

• `x/sqrt6`

• `x/sqrt8`

Answer 1

If the length of the body diagonal of a FCC unit cell is xÅ, the distance between two octahedral voids in the cell in Å is `bbunderline(x/sqrt6)`.

Explanation:

Octahedral voids are present at the body centre and edge centre.

Distance between octahedral void = `a/sqrt2`

Length of body diagonal = `sqrt3a`

x = `sqrt3a`

a = `x/sqrt3`

Distance = `a/sqrt2`

= `(x/sqrt3)/sqrt2`

= `x/(sqrt3 xx sqrt2)`

= `x/sqrt6 A`