Question

In a simple cubic lattice of anions, the side length of the unit cell is $2.88$ $\stackrel{\circ }{A}$. The diameter of the void in the body centre is:

• A. $0.461$ $\stackrel{\circ }{A}$
• B. $2.108$ $\stackrel{\circ }{A}$
• C. $4.908$ $\stackrel{\circ }{A}$
• D. $1.284$ $\stackrel{\circ }{A}$

Answer 1

The correct option is B $2.108$ $\stackrel{\circ }{A}$

In simple cubic lattice, the atoms are present only at the corners of the cube and there is a vacant space (cubical void) in the body centre of simple cubic lattice.

In simple cubic lattice, the atoms at corner are in contact with the atoms at adjacent corners.

Here, the anions forms the simple cubic lattice. Since the adjacent anions at corners are in contact, the edge length of unit cell is " $2\times \text{Radius of anion}=2.88\stackrel{\circ }{A}$"

Body diagonal of cubic lattice =$a\sqrt{3}$
where 'a' is edge length of the cell

Diameter of the void in the body center,

$=a\sqrt{3}-(2\times \text{Radius of anion})$
$=a\sqrt{3}-a$
$=(1.732\times 2.88)-2.88$
$=4.988-2.88=2.108\stackrel{\circ }{A}$