Question

Match the symmetry elements in Group I with the corresponding crystal system in Group II. \begin{tabular}{|c|c|} \hline Group I & Group II
\hline P. 3A2, 3m, 4A3+i & 1. Orthorhombic
Q. i, 1A4, m & 2. Hexagonal
R. i, 3A2, 3m & 3. Tetragonal
S. 1A3+m, 3m, 3A2 & 4. Cubic
\hline \end{tabular}

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

Hint:

When matching symmetry elements to crystal systems, focus on the number of symmetry operations (e.g., axes of rotation) and the type of symmetry (e.g., mirror planes, inversion centers) that characterize each crystal system.

Answer 1

The Correct Option is C

Step 1: Understand the Symmetry Elements.
Each symmetry element in Group I is associated with a specific crystal system in Group II. The matching of symmetry elements with their respective crystal system depends on the types of symmetry present, such as axes of symmetry, mirror planes, and inversion centers.
Step 2: Analyze the Symmetry Elements and Crystal Systems.
- P: 3A2, 3m, 4A3+i corresponds to the Cubic crystal system (Group II - 4), as cubic symmetry involves high symmetry including threefold rotations and mirror planes.
- Q: i, 1A4, m corresponds to the Tetragonal crystal system (Group II - 3), as tetragonal symmetry includes a fourfold axis of symmetry.
- R: i, 3A2, 3m corresponds to the Orthorhombic crystal system (Group II - 1), characterized by three mutually perpendicular twofold axes.
- S: 1A3+m, 3m, 3A2 corresponds to the Hexagonal crystal system (Group II - 2), which has a sixfold axis of symmetry.
Step 3: Conclusion.
Thus, the correct matching is: \[ \text{P-4, Q-3, R-1, S-2} \] Final Answer: \[ \boxed{\text{P-4, Q-3, R-1, S-2}} \]