Question

If a solid has BCC structure and if the distance of the closest approach between the two atoms is $1.73\stackrel{\circ }{\text{A}}$. The edge length of the cell is

• A. $200\text{pm}$
• B. $\frac{\sqrt{3}}{\sqrt{2}}\text{pm}$
• C. $142.2\text{pm}$
• D. $\sqrt{2}\text{pm}$

Answer 1

The correct option is A $200\text{pm}$

The radius of the sphere in the BCC is $r_{\text{atom}}=\frac{\sqrt{3}}{4}a$. ($a=$edge length of cell)
The closest approach in BCC lattice is half of the body diagonal.
$\therefore \frac{\sqrt{3}}{2}a=1.73\stackrel{\circ }{\text{A}}\Rightarrow a=\frac{2\times 1.73}{\sqrt{3}}=\frac{2\times 1.73}{1.732}\approx 2\stackrel{\circ }{\text{A}}\approx 200\text{pm}$