Question

Distance between any two consecutive layers in cubic packing is $(a:$ edge length of cubic unit cell $)$
$A)\dfrac{{\sqrt 3 }}{4}a \\\ B)\dfrac{{\sqrt 3 }}{2}a \\\ C)\sqrt {3a} \\\ D)\dfrac{a}{{\sqrt 3 }}$

Answer 1

Hint : to measure the distance for any two consecutive layers in cubic packing we use the formula $a = 2r$ . Simple cubic packing consists of placing spheres centered on integer coordinates in Cartesian space. Arranging layers of close packed spheres such that the spheres of every third layer overlay one another gives face-centered cubic packing.

Complete Step By Step Answer:
In a cubic close-packed arrangement of atoms, the unit cell consists of four layers of atoms. The top and bottom layers contain six atoms at the corners of a hexagon and one atom at the center of each hexagon. The atoms in the third layer occupy a different set of depressions than those in the first.
Atoms in a cubic close packing structure have a coordination number of $12$ because they contact six atoms in their layer, plus three atoms in the layer above and three atoms in the layer below.
They are called face centered cubic and hexagonal close packed, based on their symmetry.
We measure the distance between any two consecutive cubic packs by using the formula.
$= a = 2r$ .
Now, let’s put the values.
$= \dfrac{{2r}}{{\sqrt 3 }}$
$\dfrac{{2a}}{{2\sqrt 3 }}$
$= \dfrac{a}{{\sqrt 3 }}$
So, the correct answer is $D)\frac{a}{{\sqrt 3 }}$ .

Note :
The most efficient packing arrangement is Closest Packing, The most efficient conformation atomic spheres can take within a unit cell is known as the closest packing configuration. Densely packed atomic spheres exist in two modes: hexagonal closest packing and cubic closest packing.