Question

Which of the following statements is/are correct about tetrahedral voids in an fcc unit cell? Given that the length of the edge of the unit cell is ‘a’ pm and of body diagonal is ‘b’ pm.
A) Each tetrahedral voids lies at a distance of $\dfrac{b}{4}$ from the nearest corner
B) Each tetrahedral voids lies at a distance $\dfrac{3b}{4}$ from the farthest corner
C) Each tetrahedral voids lies at a distance $\dfrac{\sqrt{3}a}{4}$ from the nearest corner
D) The distance between two tetrahedral voids is $\dfrac{b}{2}$

Answer 1

Hint: The answer here is based on the concept of crystallography that deals with various types of crystal lattice and also the distance, cell length and angles between them. For fcc, the assigned distances for tetrahedral void is to be found.

Complete step by step answer:
The concepts of the crystallography in chemistry basically in inorganic chemistry are familiar to us and also several parameters associated with them.
Now we shall see what is fcc and how are tetrahedral voids arranged in it.
- The simple cubic unit cell is the repeating units present in the shape of a cube and thus the name.
- Face centered cubic lattice is one of the Bravais lattices that is an arrangement of atoms in crystals in which the atomic centres are displaced in space in such a way that one atom is located at each corner of the cube and one at the center of the face.
- Voids are nothing but the empty spaces and tetrahedral voids refers to a total of eight voids in the fcc unit cell as there are eight corners.
In this fcc unit, if we consider length of the edge of the unit cell is ‘a’ pm and of body diagonal is ‘b’ pm according to the question, then each tetrahedral voids lies at a distance of $\dfrac{b}{4}$ from the nearest corner and also at a distance $\dfrac{3b}{4}$ from the farthest corner.
Also each tetrahedral void lies at a distance $\dfrac{\sqrt{3}a}{4}$ from the nearest corner.
Here the distance between two tetrahedral voids will be $\dfrac{b}{2}$

Therefore, all the options given in this question are correct.

Note: Note that apart from the tetrahedral voids, there are also octahedral voids in the fcc unit cell. Since there is one tetrahedral void in each edge and one edge is shared by 4 lattices, only 1/4th of the void is effectively inside the lattice and hence the total number of octahedral voids in fcc are 4.