Question

A crystal (of an element 'X') has a bcc structure. It has an edge length of $4.3\stackrel{\circ }{A}$. The shortest distance between the atoms is:

• A. $1.86\stackrel{\circ }{A}$
• B. $4.3\stackrel{\circ }{A}$
• C. $3.72\stackrel{\circ }{A}$
• D. $7.44\stackrel{\circ }{A}$

Answer 1

The correct option is C $3.72\stackrel{\circ }{A}$

Given, a crystal has a body centred cubic structure. The edge length of the cell is $4.3\stackrel{\circ }{A}$

In bcc, atoms are aligned along the body diagonal by touching each other. The distance of nearest atom in bcc were between corner atoms and body centred atom. The body diagonal of the bcc is shown below,

We know, for bcc
$\text{Distance of nearest atom 'd'}=\frac{\sqrt{3}a}{2}$
$=\frac{1}{2}\times \sqrt{3}a=\frac{\sqrt{3}}{2}\times 4.3=3.72\stackrel{\circ }{A}$