Question

In a monoclinic unit cell, the relation of sides and angles are, respectively:
(A) \[{{a = b }} \ne {{ c \quad and \quad \alpha = \beta = \gamma = 9}}{{{0}}^{\text{o}}}\]
(B) \[{{a }} \ne {{ b }} \ne {{ c \quad and \quad \alpha = \beta = \gamma = 9}}{{\text{0}}^{\text{o}}}\]
(C) \[{{a }} \ne {{ b }} \ne {{ c \quad and \quad \beta = \gamma = 9}}{{{0}}^{{o}}} \ne {{\alpha }}\]
(D) \[{{a}} \ne {{ b}} \ne {{ c \quad and \quad \alpha }} \ne {{\beta }} \ne {{\gamma }} \ne {{ 9}}{{{0}}^{{o}}}\]

Answer 1

Hint: Monoclinic crystal system has a restriction on two of the angles. It forms a rectangular prism having a base of parallelogram.

Complete step-by-step solution:
In crystallography, the crystal system is classified into seven groups on the basis of structures of the crystal. Symmetry here describes the relationship between the sides of the unit cell a, b and c and angles $\alpha$, $\beta$ and $\gamma$. These are- Triclinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal and Cubic.
As per question, in a monoclinic system, all three axes are unequal in length and any two axes are perpendicular to each other and the third is inclined between them forming an oblique angle \[{{\alpha }}\]. Rest of the two angles are \[{\text{9}}{{\text{0}}^{\text{o}}}\]each.


Hence, the correct option is (C).

Additional information: It is also known as sphenoidal because its general form is sphenoid. But it also exists in domatic and prismatic form. It depicts a 2-fold rotation axis and a single mirror plane.

Note: We can also understand it by the meaning of the term ‘monoclinic’. It means single inclination i.e., one axis of the unit cell is inclined at an angle greater than \[{\text{9}}{{\text{0}}^{\text{o}}}\]. They can perform perfect cleavage in at least one direction.