Doubt in solid state

#1


Q no.15

#2

ABC ABC packing is hexagonal closed packing.

Tetrahedral voids:
We know that the distance between tetrahedral void and a vertex is d = √3a/4.
Also, the tetrahedral angle is cos inverse of 1/√3.
Thus the projection of d on any sides is a/4. Similarly the other tetrahedral voids will also be a/4 away from it's vertex. Thus, the distance between two consecutive tetrahedral voids is a/2

Octahedral Voids:
The distance between two nearest octahedral voids in closed packing is the distance between an edge-center and the body-center which is simply a*cos(45)
Thus the distance between two consecutive octahedral voids is a/√2.

So, therefore the correct answer is 2.