Match List I with List II

Choose the correct answer from the options given below:

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

The correct answer is option 1. (A)-(IV), (B)-(I), (C)-(II), (D)-(III).

(A) Simple and face centred cubic: (IV) belong to the same crystalline system:

Both simple cubic and face-centered cubic (FCC) belong to the same crystalline system: the cubic crystal system. The cubic crystal system is defined by having all three unit cell lengths (a, b, and c) equal and all three angles between the axes (α, β, and γ) equal to 90 degrees. This creates a basic cubic unit cell.

Simple cubic places an atom at each corner of the unit cell.

Face-centered cubic places atoms at each corner and in the center of each face of the unit cell.

Even though they arrange atoms differently within the unit cell, both simple cubic and FCC follow the fundamental characteristics of the cubic crystal system.

(B) Cubic and rhombohedral: (I) \(a = b = c\)

The statement "Cubic and rhombohedral \(a = b = c\)" refers to two different crystal systems in crystallography: the cubic system and the rhombohedral system.

Cubic System: In the cubic system, all three axes are of equal length (\(a = b = c\)) and intersect each other at right angles (90 degrees). This system includes three main types of lattice structures: simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC).

Rhombohedral System: In the rhombohedral system, all three axes are of equal length (\(a = b = c\)) but they are not perpendicular to each other. Instead, they intersect at oblique angles, typically larger or smaller than 90 degrees. In this system, the unit cell is rhombohedral in shape.

It's important to note that even though both systems have equal lengths for all three axes (\(a = b = c\)), they differ in the angles between these axes. In the cubic system, the angles are all 90 degrees, while in the rhombohedral system, the angles are not necessarily 90 degrees.

So, while both systems share the characteristic of having equal axis lengths, they belong to different crystal systems due to their differences in the angles between axes.

(C) Cubic and tetragonal : (II) \(\alpha = \beta = \gamma = 90^o\) :

The statement "Cubic and tetragonal \(\alpha = \beta = \gamma = 90^\circ\)" refers to two different crystal systems in crystallography: the cubic system and the tetragonal system.

Cubic System: In the cubic system, all three axes (\(a\), \(b\), and \(c\)) are of equal length (\(a = b = c\)), and they intersect each other at right angles, with all angles equal to \(90^\circ\). This system includes structures like simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC).

Tetragonal System: In the tetragonal system, two of the axes (\(a\) and \(b\)) are of equal length (\(a = b\)), but the third axis (\(c\)) is of a different length, and all three axes intersect each other at right angles (\(\alpha = \beta = \gamma = 90^\circ\)). This system has a tetragonal unit cell, which is a rectangular prism with square base faces.

In both systems, the angles between the axes are \(90^\circ\), but the lengths of the axes differ. In the cubic system, all three axes are of equal length, while in the tetragonal system, only two of the axes are equal in length, and the third axis is different.

So, while both systems have equal angles between axes, they belong to different crystal systems due to their differences in axis lengths.

(D) Hexagonal and monoclinic : (III) have only two cystallographic angle of \(90^o\):

Hexagonal and monoclinic are two different crystal systems and both have two of their crystallographic angle of 90º.