Solid State - Result Question 2

####2. An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is

(2019 Main, 12 April I)

(a) 2a

(b) a

(c) a2

(d) 32a

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Answer:

Correct Answer: 2. (c)

Solution:

  1. In fcc unit cell, two tetrahedral voids are formed on each of the four non-parallel body diagonals of the cube at a distance of 3a/4 from every corner along the body diagonal.

The angle between body diagonal and an edge is cos1(1/3). So, the projection of the line on an edge is a/4. Similarly, other tetrahedral void also will be a/4 away. So, the distance between these two is [aa4]a4=a2.



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