Question

The number of distinct space groups possible in 3-dimensions is:

• A. 240
• B. 220
• C. 230
• D. 250

Hint:

Certain fundamental numbers in crystallography are worth memorizing for competitive exams:

7 Crystal Systems (e.g., cubic, tetragonal)
14 Bravais Lattices
32 Crystallographic Point Groups
230 Space Groups (in 3D)
These are often asked as direct factual questions.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a factual question about the mathematical classification of crystal symmetries. A space group is the complete symmetry group of a crystal, including all translational symmetries (lattice translations, glide planes, screw axes) and point group symmetries (rotations, reflections, inversions). The question asks for the total number of unique space groups that can exist in a three-dimensional periodic structure.
Step 2: Detailed Explanation:
The derivation of the number of space groups is a complex task in mathematical crystallography. It involves combining the 14 fundamental Bravais lattices with the 32 possible crystallographic point groups. The combination of translational symmetry operations (like screw axes and glide planes) with the point group operations leads to a finite and specific number of possible unique space groups.
Through systematic enumeration, it was proven in the late 19th century that there are exactly 230 distinct space groups in three dimensions. This is a fundamental result in the field of crystallography.
Step 3: Final Answer:
There are 230 distinct space groups possible in 3-dimensions.