Question

In an ionic crystal a form of cubic close packing (CCP) and B atom are present at every tetrahedral void. If any sample of crystal contains 'N' number of B atom then number of a atom in that sample is:
(A) N
(B) $\dfrac{N}{2}$
(C) $2N$
(D) $\sqrt{2}N$

Answer 1

Hint : We know that there are two types of two-dimensional packing such as square close packing and hexagonal close packing whereas in three dimensions it is three types namely, hexagonal close packing, Cubic close packing, and body-centered cubic close packing.

Complete Step By Step Answer:
The unit cell is the smallest group of atoms that has the overall symmetry of a crystal, and from which the entire lattice can be built up by repetition in three dimensions. When we arrange a unit cell in all dimensions, we obtain a structure of the crystal. The properties of the unit cell can be measured by the length of edges and the angle of joining the edges. Now let us discuss cubic close packing in three dimensions to find the coordination number, Cubic close packing: In cubic close packing when the third layer is placed above the second layer in such a manner that its sphere covers the octahedral voids and the sphere of the third layer is not aligned with the first or the second layer, This arrangement is known as type.
Close packing in crystals also refers to as a close packing in solids which is defined as the efficient arrangement of constituent particles in a crystal defined as the efficient arrangement of constituent particles in a crystal lattice in a vacuum. We have to assume that all particles (atoms, molecules, and ions) are of the same spherical solid form to understand this set more clearly. So a cubic shape is the unit cell of a lattice. Now, there will still be some empty spaces when we stack spheres in the cell. The arrangement of these spheres has to be very effective to reduce these empty spaces. Tetrahedral void is double the number of atoms in CCP. Hence, the number of atoms of B will be double to the number of atoms of A. By given that the number of B atoms $=N$ hence, the number of A atoms $=N/2.$
Therefore, the correct answer is option B.

Note :
Remember that the close packing in crystals refers to the space-efficient arrangement of constituent (such as atoms, molecules, and ions) particles in a crystal lattice. The unit cell of the crystal is defined by the lattice points.