If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive a relation between r and R.
Draw a diagram showing octahedral void and derive the relation between r and R.

Explanation

Derivation of relation between r and R
A sphere fitted into the octahedral void is shown by shaded circle. The spheres present in other layers are not shown in the figure.

`:. DeltaABC` is a right angled triangle.
`:.` We apply pythagoras theorem
`AC^(2)=AB^(2)+BC^(2)`
`(2R)^(2)=(R+r)^(2)+(R+r)^(2)=2(R+r)^(2)`
`4R^(2)=2(R+r)^(2), 2R^(2)=(R+r)^(2)`
`sqrt(2(R )^(2))=sqrt((R+r)^(2)) , sqrt(2)R=R+r`
`r= sqrt(2)R-R`
`r=(sqrt(2)-1)R`
`r= (1.414 -1)R`
`r=0.414R`