Question

An element has $ABAB..$ type close-packed structure and radius of an atom of elements is $300pm$ what is the distance between two adjacent layers?
A) $~600~\sqrt{\dfrac{2}{3}}pm$
B) $1200~\sqrt{\dfrac{3}{2}}pm$
C) $1200~\sqrt{\dfrac{2}{3}}pm$
D) $600~\sqrt{\dfrac{3}{2}}pm$

Answer 1

We know that the different packing structure type can be identified on basis of molecular arrangement in given lattice which is of each type of a packing structure have unique arrangement of the atom within them that can be understood by view lattice from side profile. Here the predefined formula for distance between two adjacent layers is given by; $r\times 2\times \sqrt{\dfrac{2}{3}}$.

Complete answer:
Let us now define the atomic radius. The atomic radius of an element refers to the measure of the size of the element’s atoms, which is typically the mean distance from the nucleus center to the boundary of its surrounding shells of the electrons. However, since the boundary is not well-defined of the atomic radius. There are three types of atomic radii which are Van der Waals radius, covalent radius and ionic radius.

Hexagonal close packing is packing structure in which lattice layers are arranged in form of $ABAB$ where each letter signifies individual lattice configuration as well as collection of lattice form closed packing structure. In hexagonal close packing top along with bottom lattice is similar with geometry of hexagon.

Atom is placed on vertices as well as in center of hexagon and middle layer have triangle geometry where atom is placed on vertices of triangle because of geometry any atom in given hexagonal close packing structure will be surrounded by $4$ atoms in same lattice as of concerned atom by $4$ atom in lattice above atom along by $4$ atoms in lattice below atom. Here we have radius $(r)=300$

The distance between the two layers is
$=r\times 2\times \sqrt{\dfrac{2}{3}}$
Now by just substituting the values in above formula we get;
​$=300\times 2\sqrt{\dfrac{2}{3}}$
On further simplification;
$\Rightarrow 600\times \sqrt{\dfrac{2}{3}}$

Therefore, Option A is correct answer i.e. distance between these two adjacent layers $600\times \sqrt{\dfrac{2}{3}}$

Note: Note that the coordination number of any type of unit cell is a characteristic property of the structure along with that never change in any condition. Even though we have experienced certain anomalies which are explaining coordination numbers meanwhile explaining crystal defects.