Question

For the orthorhombic system, axial ratios are $a\ne b\ne c$ and the axial angles are:
A.$\alpha =\beta =\gamma \ne {90}^{\circ }$
B.$\alpha =\beta =\gamma ={90}^{\circ }$
C.$\alpha =\gamma ={90}^{\circ },\beta \ne {90}^{\circ }$
D.$\alpha \ne \beta \ne \gamma ={90}^{\circ }$

Answer 1

Hint:Orthorhombic system is a type of crystal system which is used to describe the structure of crystalline solids. In such a system, the three axes are unequal in length and mutually perpendicular to each other.

Complete step by step answer:
There are seven types of crystals that are used to describe the structure of crystalline solids, one of which is an orthorhombic crystal system.
The unit cell of any type of crystal is determined by the length of the three dimensions, i.e., length, breadth and height of the crystal; and the set of three angles between any of the two sides.
Three dimensions of the crystal lattice are denoted as a, b and c and the angles between these axes are $\alpha ,\beta$ and $\gamma$.
In an orthorhombic crystal system, the three sides are unequal in length and the angles between any two sides is ${90}^{\circ }$. That is, all the six faces are rectangular in shape.
So, we can write $a\ne b\ne c$ and $\alpha =\beta =\gamma ={90}^{\circ }$.

Hence option B is correct.

Note:
The other types of crystals are cubic, trigonal, tetragonal, hexagonal, monoclinic and triclinic. For these crystals the axial ratio and axial angles are as follows:
Cubic: $a=b=c$ and $\alpha =\beta =\gamma ={90}^{\circ }$
Trigonal: $a=b=c$ and $\alpha =\beta =\gamma \ne {90}^{\circ }$
Tetragonal: $a=b\ne c$ and $\alpha =\beta =\gamma ={90}^{\circ }$
Hexagonal: $a=b\ne c$ and $\alpha =\beta ={90}^{\circ },\gamma ={120}^{\circ }$
Monoclinic: $a\ne b\ne c$ and $\alpha =\gamma ={90}^{\circ },\beta \ne {90}^{\circ }$
Triclinic: $a\ne b\ne c$ and $\alpha \ne \beta \ne \gamma$