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Question

In a simple cubic lattice of anions, the side length of the unit cell is 3.0 oA. The diameter of the void in the body centre is

A
0.46 oA
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B
2.2 oA
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C
4.9 oA
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D
1.7 oA
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Solution

The correct option is B 2.2 oA
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 =a3

The body diagonal contains 2 radii of lattice atoms and the diameter (2R) of central cubical void
Length of body diagonal=a3=2r+2Ra+D
Diameter of the void in the body center,
D=a3a
=(33)3
=3(31)=2.2 oA

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