Question

An element crystallizes in bcc lattice. The atomic radius of the element is 2.598 \AA. What is the volume (in cm$^3$) of one unit cell?

• A. $6.4 \times 10^{-22}$
• B. $2.16 \times 10^{-20}$
• C. $2.16 \times 10^{-22}$
• D. $2.16 \times 10^{-24}$

Hint:

For bcc lattice, use $a = \dfrac{4r}{\sqrt{3}}$ to find unit cell volume from atomic radius.

Answer 1

The Correct Option is C

For bcc, relation between radius $r$ and edge length $a$ is: $a = \dfrac{4r}{\sqrt{3}}$
$r = 2.598 \ \text{\AA} = 2.598 \times 10^{-8} \ \text{cm}$
$a = \dfrac{4 \times 2.598 \times 10^{-8}}{\sqrt{3}} \approx 5.996 \times 10^{-8} \ \text{cm}$
Volume of unit cell = $a^3 = (5.996 \times 10^{-8})^3 \approx 2.16 \times 10^{-22} \ \text{cm}^3$