Question

Consider a cube 1 of Body Centered Cubic unit cell of edge length a now atom at the body center can be viewed to be lying on the corner of another cube 2.Find the volume common to cube 1 and cube 2.

• A. $\frac{a^{3}}{27}$
• B. $\frac{a^{3}}{64}$
• C. $\frac{a^{3}}{2\sqrt{2}}$
• D. $\frac{a^{3}}{8}$

Answer 1

Answer: (D)

$\frac{a^{3}}{8}$

Answer 2

Common Volume = $\left( \frac{a}{2} \right)^{3}$ =$\frac{a^{3}}{8}$

[\ Common vol is a cube of edge length $\frac{a}{2}$]