Question

An element has ABAB..... type close-packed structure. The radius of an atom of the element is 300 pm. What is the distance between two adjacent layers?
 Options
A.\[600\sqrt {\dfrac{2}{3}} pm\]
B.\[1200\sqrt {\dfrac{2}{3}} pm\]
C.\[1200\sqrt {\dfrac{3}{2}} pm\]
D.\[600\sqrt {\dfrac{3}{2}} pm\]

Answer 1

Hint: Crystal structure is a representation of the orderly arrangement of atoms, ions, or molecules in a crystalline substance used in crystallography. The inherent composition of the constituent particles results in symmetric patterns that replicate along the principal directions of three-dimensional space in matter, forming ordered structures.

Complete answer:
The unit cell of the system is the smallest group of particles in the substance that makes up this repeated sequence. The symmetry and composition of the whole crystal are fully reflected in the unit cell, which is made up by repeated translation of the unit cell along its principal axes. The nodes of the Bravais lattice are described by the translation vectors.
 Crystal structure is a representation of the orderly arrangement of atoms, ions, or molecules in a crystalline substance used in crystallography. The inherent composition of the constituent particles results in symmetric patterns that replicate along the principal directions of three-dimensional space in matter, forming ordered structures.
Hexagonal close packing:
The second row can be staggered below the first row, with the spheres fitting into the depressions of the first row. As a result, if we refer to the first row as a "A" type row, the second row, which is organised differently, can be referred to as a "B" type row. The third row displays as “A” form once more. The “ABAB” sort of packing is what it's called. Each sphere is in contact with six other spheres in this configuration. As a result, it has a teamwork number of six. When the centres of the six closest neighbouring spheres are connected, a hexagon is formed. Hexagonal close packing in two dimensions is the name given to this type of solid packing. In contrast to square close packing, it has less free space and hence better packing efficiency.
The distance between the two layers is given by the formula = \[2r\sqrt {\dfrac{2}{3}} pm\]
Here r = 300 pm
So, Distance = \[2(300)\sqrt {\dfrac{2}{3}} pm\]
= \[600\sqrt {\dfrac{2}{3}} pm\]

Note:
 The second row can be staggered below the first row, with the spheres fitting into the depressions of the first row. As a result, if we refer to the first row as a "A" type row, the second row, which is organised differently, can be referred to as a "B" type row. The third row displays as “A” form once more. The “ABAB” sort of packing is what it's called. Each sphere is in contact with six other spheres in this configuration. As a result, it has a teamwork number of six. When the centres of the six closest neighbouring spheres are connected, a hexagon is formed. Hexagonal close packing in two dimensions is the name given to this type of solid packing. In contrast to square close packing, it has less free space and hence better packing efficiency.