Question

A solid has a bcc structure. If the distance of closest approach between the two atoms is $1.73\stackrel{o}{A}$. The edge length of the cell is:

• A. $199$pm
• B. $\sqrt{3/2}$ pm
• C. $142.2$pm
• D. $\sqrt{2}$pm

Answer 1

The correct option is A $199$pm

In bcc structure, the atoms are present at corners and at body center and the atoms along the body diagonal are touching each other.

So, if $a$ is the edge length of the cube and $r$ is the radius of the atom.

Then, $\sqrt{3}a=4r$

$\Rightarrow 2r=\frac{\sqrt{3}a}{2}$

Now, distance of closest approach is reached when two atoms are touching each other i.e their centers are at $2r$ distance from each other.

So, $\frac{\sqrt{3}}{2}a=1.73\mathring{A}$

$\Rightarrow a=\frac{1.73\times 2}{\sqrt{3}}\mathring{A}=1.99\mathring{A}=199pm$

Option A is correct.