Question

The elements of symmetry in a crystal are:
A.Plane of symmetry
B.Axis of symmetry
C.Centre of symmetry
D.none of these

Answer 1

All crystals possess a regular, repetitive internal structure. In order to solve this question, you need to recall the concept of symmetry in crystals which describes the repetition of structural features. The point or plane of reference used to describe the symmetry gives rise to different classifications of symmetry.

Complete step by step solution:
Broadly, there exist two types of symmetry, namely translational symmetry and point symmetry.
Point symmetry describes the repetition of a structural feature around a point. Point symmetry is further of three types that are, reflection, rotation and inversion.
Reflection occurs when a motif on one side of a plane passing through the centre of the crystal is the mirror image of a motif which appears on the other side of the plane. We can visualise it as an imaginary plane which passes through the centre of a crystal and divides it into two equal portions such that one part is exactly the mirror image of the other. We can say that the element of symmetry here is a plane of symmetry.
Rotational symmetry arises when a structural element is rotated a fixed number of degrees about a central axis before it is repeated. In other terms, it is an imaginary straight line about which, if the crystal is rotated, it will present the same appearance more than once during the complete revolution. We can say that the element of symmetry here is the axis of symmetry.
Inversion symmetry is possessed by a crystal, if every line drawn through the center of the crystal will connect two identical features on the opposite sides of the crystal. We can visualise it as an imaginary point within the crystal that any line drawn through it intersects the surface of the crystal at equal distances in both directions. It can be said as the centre of symmetry.

Thus, the correct options are A, B and C.

Notes:
Overall, the total number of planes, axes and centre of symmetry are known as elements of symmetry.
Planes of symmetry = 9
Axis of symmetry = 13
Centre of symmetry = 1
Total number of elements of symmetry are = 23
A cubic crystal possesses all 23 elements of symmetry.