Question

A body centred cubic lattice is made up of hollow spheres of $B$. Spheres of solid $A$ are present in hollow spheres of $B$. Radius of $A$ is half of radius of $B$. What is the ratio of total volume of spheres of $B$ unoccupied by $A$ in a unit cell and volume of unit cell?

• A. $\frac{7\sqrt{3\pi }}{64}$
• B. $\frac{7\sqrt{3}}{128}$
• C. $\frac{7\pi }{64}$
• D. None of the above

Answer 1

The correct option is D None of the above

As we know for a BCC,
ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell $=2\ast 4/3\pi \left(\sqrt{(}3\right)/4{)}^3-2\ast 4/3\pi \left(\sqrt{(}3\right)/8{)}^3/1$