Question

In which of the following systems, interfacial angles α =γ=${{90}^{\circ }}$but β≠${{90}^{\circ }}$?
(A)Monoclinic
(B)Rhombohedral
(C)Triclinic
(D)Hexagonal

Answer 1

Hint: Monoclinic, rhombohedral, triclinic, hexagonal are one of the types of seven crystal systems of crystalline solid proposed by a French mathematician Bravais.
- On the basis of the classification symmetry, the crystal has been divided into seven systems. These can be grouped into which are regrouped into seven crystal systems. These seven systems have divided on the bases of the characteristics of their axial angle and intercepts.

Complete Solution :
On the basis of axial or primitive distance and interfacial angle there are mainly seven types of crystalline system found in the crystalline solid. These crystalline systems differ in the length of the unit cell (the smallest repeating portion of a crystalline substance which shows the complete geometry of the crystalline substance) edges (a, b and c) and the angles (α, β and γ) between the unit cell edges.
(A) In monoclinic crystal system all the sides are of different lengths (i.e. a ≠ b ≠ c), while two edge angles are similar but one is different (i.e. α = γ = ${{90}^{\circ }}$ but β≠${{90}^{\circ }}$). This type of crystalline geometry found in the crystalline solid of monoclinic sulphur and washing soda $\text{(N}{{\text{a}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}.\text{10}{{\text{H}}_{\text{2}}}\text{O)}$ .

(B) In a rhombohedral or trigonal crystal system all the sides are of same lengths (i.e. a = b = c), while all edge angles are similar. (i.e.α =β = γ ≠${{90}^{\circ }}$). This type of crystalline system is found in $\text{CaC}{{\text{O}}_{\text{3}}}$ and$\text{HgS}$.

(C) In triclinic crystal system all the sides are of different lengths (i.e. a ≠ b ≠ c), while all the edge angles are different and not equal to ${{90}^{\circ }}$ (i.e. α ≠ β ≠ γ ≠${{90}^{\circ }}$). $\text{CuS}{{\text{O}}_{\text{4}}}\text{.5}{{\text{H}}_{\text{2}}}\text{O}$ and ${{\text{K}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}$ is the example of triclinic system.

(D) In a hexagonal crystal system two sides of an edge are the same while one is different (i.e. a = b ≠ c), while two edge angles are similar and one is different. (i.e.α =β =${{90}^{\circ }}$, γ =${{120}^{\circ }}$). This type of crystalline system is found in graphite and $\text{ZnO}$.
So, the correct answer is “Option A”.

Note: In the cubic and trigonal (rhombohedral) system, the three unit edges are of equal length but for the rest five systems it is not.
- All the interfacial angles are ${{90}^{\circ }}$ in the cubic, tetragonal and orthorhombic system but not in the rest of the five crystal system.