Question

A solid has 'BCC' structure. If the distance of nearest approach between two atoms is 1.73 A, the edge length of the cell is:

• A. 314.20 pm
• B. 216 pm
• C. 200 pm
• D. 141 pm

Answer 1

The correct option is C 200 pm

In BCC structure, the atoms are present on corners of cubic unit cell and one on the body center in such a way that the atoms on the corners and body center are touching each other.

If $a$ is the edge length of cube and $r$ is the radius of each atom.

Distance of nearest approach between two atoms $=2r=1.73\mathring{A}$

And we have $\sqrt{3}a=4r$

$\Rightarrow a=\frac{4r}{\sqrt{3}}=\frac{2\times 1.73}{\sqrt{3}}=2\mathring{A}=200pm$