Question

The maximum radius of sphere that can be fitted in the octahedral hole of cubical closed packing of sphere of radius $r$ is:

• A. $0.732r$
• B. $0.225r$
• C. $0.155r$
• D. $0.414r$

Answer 1

The correct option is D $0.414r$

For octahedral voids, $r+r_1=2r\cdot \frac{1}{\sqrt{2}}$

$⟹\frac{r_1}{r}=\sqrt{2}r$

$⟹\frac{r_1}{r}=\sqrt{2}-1=0.414$

$⟹r_1=0.414r$