Question

The ratio of the distances with the nearest neighbours in a body centered cubic (BCC) and a face centered cubic (FCC) crystals with the same unit cell edge length is:

• A. $\sqrt{\frac{3}{2}}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\sqrt{\frac{3}{2}}$

Nearest neighbour distance in BCC crystal $\left(r^{+}{r}^{-}\right)=\frac{\sqrt{3}a}{2}$
Nearest neighbour distance in FCC crystal $\left(r^{+}{r}^{-}\right)=\frac{\sqrt{2}a}{2}$

Given: Edge length (a) is the same in both the BCC and the FCC crystal.
Thus, $\text{ratio}=\frac{\frac{\sqrt{3}a}{2}}{\frac{\sqrt{2}a}{2}}=\frac{\sqrt{3}}{\sqrt{2}}=\sqrt{\frac{3}{2}}$