Question

Radius of an octahedral void relative to the radius of the spheres in a close packing is:

• A. $1.414$
• B. $0.225$
• C. $1.225$
• D. $0.414$

Answer 1

The correct option is D $0.414$

In the adjoining figure,
$B{C}^2=A{B}^2+A{C}^2$

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

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

$\sqrt{2}R=R+r$

$r=0.414R$

Option D is correct.