Question

In a simple cubic lattice of anions, the side length of the unit cell is $3.0\stackrel{o}{A}.$ The diameter of the void in the body centre is

• A. $0.46\stackrel{o}{A}$
• B. $2.2\stackrel{o}{A}$
• C. $4.9\stackrel{o}{A}$
• D. $1.7\stackrel{o}{A}$

Answer 1

The correct option is B $2.2\stackrel{o}{A}$

In a simple cubic lattice, the atoms are present at the eight corners of the cube and they touching each other on the edges such that a = 2r
Where,
a is the edge length of the cube
r is the radius of the sphere/atom

Here, the vacant space in body centre is surrounded by eight atoms at corners. Hence, it is a cubical void.

Body diagonal of cubic lattice $=a\sqrt{3}$

The body diagonal contains 2 radii of lattice atoms and the diameter (2R) of central cubical void
Length of body diagonal$=a\sqrt{3}=2r+2R\Rightarrow a+D$
Diameter of the void in the body center,
$D=a\sqrt{3}-a$
$=\left(3\sqrt{3}\right)-3$
$=3(\sqrt{3}-1)=2.2\stackrel{o}{A}$