Question

Match the crystal systems in Column I with the corresponding axial lengths \(a, b, c\) and interaxial angles \(\alpha, \beta, \gamma\) provided in Column II.

Column I	Column II
(P) Tetragonal	(1) \(a \neq b \neq c,\ \alpha = \beta = \gamma = 90^{\circ}\)
(Q) Rhombohedral	(2) \(a = b \neq c,\ \alpha = \beta = \gamma = 90^{\circ}\)
(R) Orthorhombic	(3) \(a \neq b \neq c,\ \alpha = \gamma = 90^{\circ} \neq \beta\)
(S) Monoclinic	(4) \(a = b = c,\ \alpha = \beta = \gamma \neq 90^{\circ}\)

• A. P-3, Q-1, R-2, S-4
• B. P-2, Q-3, R-4, S-1
• C. P-4, Q-3, R-2, S-1
• D. P-2, Q-4, R-1, S-3

Hint:

Compare the number of equal axes and the number of 90 degree angles each crystal system has with the Column II descriptions.

Answer 1

The Correct Option is D

Step 1: Recall the seven crystal systems and their axial relations.
Every crystal system is fixed by its three axial lengths \(a\), \(b\), \(c\) and its three interaxial angles \(\alpha\), \(\beta\), \(\gamma\). We check each letter in Column I against the definitions used in crystallography and pick the matching entry in Column II.

Step 2: Match P (Tetragonal).
A tetragonal cell has two equal axes and one different axis, with all three angles fixed at 90 degrees. This is \(a = b \neq c,\ \alpha = \beta = \gamma = 90^{\circ}\), which is entry (2). So P-2.

Step 3: Match Q (Rhombohedral).
A rhombohedral cell has all three axes equal in length and all three angles equal to each other but different from 90 degrees. This is \(a = b = c,\ \alpha = \beta = \gamma \neq 90^{\circ}\), which is entry (4). So Q-4.

Step 4: Match R (Orthorhombic).
An orthorhombic cell has three unequal axes but all angles fixed at 90 degrees, written \(a \neq b \neq c,\ \alpha = \beta = \gamma = 90^{\circ}\), which is entry (1). So R-1.

Step 5: Match S (Monoclinic).
A monoclinic cell has three unequal axes, two angles fixed at 90 degrees and the third angle different from 90 degrees, written \(a \neq b \neq c,\ \alpha = \gamma = 90^{\circ} \neq \beta\), which is entry (3). So S-3.

Step 6: Combine and check against the options.
The complete match is P-2, Q-4, R-1, S-3, which is exactly option (D).
\[ \boxed{P\text{-}2,\ Q\text{-}4,\ R\text{-}1,\ S\text{-}3} \]