Question

If the radius of an octahedral void is r and radius of atoms in close packing is $R$, the relation between r and $R$ is:

• A. $r=0.414R$
• B. $R=0.414r$
• C. $r=2R$
• D. $r=\sqrt{2}R$

Answer 1

Answer: (A)

$r=0.414R$

Here, the radius of the atom is $R$ and the radius of the void is $r$.

In $△ABC,$

By applying Pythagoras Theorem,

${AB}^2+{AC}^2={BC}^2$

${(R+r)}^2+{(R+r)}^2={\left(2R\right)}^2$

${2(R+r)}^2={4R}^2$
${(R+r)}^2={2R}^2$

On solving the above equation, we get-

$r=(\sqrt{2}-1)R$

$r=(1.414-1)R$

$r=0.414R$

So, option A is the correct answer.