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Question: Which primitive cell has unequal edge lengths \[\left( {{\text{a}} \ne {\text{b}} \ne {\text{c}}} \r...

Which primitive cell has unequal edge lengths (a≠b≠c)\left( {{\text{a}} \ne {\text{b}} \ne {\text{c}}} \right) and all axial angles different from 90∘{90^ \circ } ?
A.Tetragonal
B.Hexagonal
C.Monoclinic
D.Triclinic

Explanation

Solution

To solve this question, you need an idea of solid state chemistry. In different solid ionic compounds, there is a unit cell, which is the smallest group of atoms arranged in a symmetrical manner and this unit cell on repetition in all the three dimensions can build up the entire lattice. A primitive cell is the smallest possible unit cell of a lattice. While the hexagonal and tetragonal lattice has only two sides equal to each other, monoclinic and triclinic have all its sides unequal.

Complete step by step answer:
Each crystalline compound has 12 edges and 12 interfacial angles which defines the structure of the compound. The different lattices are classified on the basis of their edge lengths a, b, and c and their interfacial angles α,β,γ\alpha ,\beta ,\gamma .
For a tetragonal lattice, a=b≠ca = b \ne c and α=β=γ=90∘\alpha = \beta = \gamma = {90^ \circ }
For Hexagonal lattice, a=b≠ca = b \ne c and α=β=90∘,γ=120∘\alpha = \beta = {90^ \circ },\gamma = {120^ \circ }
For monoclinic lattice, a≠b≠ca \ne b \ne c and α=β=90∘,γ≠90∘\alpha = \beta = {90^ \circ },\gamma \ne {90^ \circ }
For triclinic lattice,a≠b≠ca \ne b \ne c and α≠β≠γ\alpha \ne \beta \ne \gamma
Among the given options, for the triclinic lattice, all the sides have different lengths and all the interfacial angles are also different from 90∘{90^ \circ }.

Hence, the correct option is option D.

Note:
The regular arrangement of building blocks (such as molecules, ions, atoms) in an ionic solid is called a “Lattice” and the smallest crystal lattice that repeats itself in a solid is called the “Unit Cell”. Each atom/molecule/ion in a compound forms the edge of the unit cell and is shared by 8 other unit cells.
In total there are 7 unit cells also called as the primitive unit cells and 14 lattice systems which define the structure of the different solids and these are known as the Bravais Lattices.