Question

Arrange the following systems in decreasing order of number of lattices in it.
A. Triclinic
B. Orthorhombic
C. Tetragonal
D. Cubic
Choose the correct answer from the options given below :

• A. A, B, D, C
• B. B, C, D, A
• C. C, D, A, B
• D. B, D, C, A

Hint:

A quick mnemonic for the number of Bravais Lattices in the 7 crystal systems (C-T-O-H-R-M-T): 3-2-4-1-1-2-1. Orthorhombic is the "most versatile" because it allows for all 4 possible centering variations without violating its symmetry!

Answer 1

The Correct Option is D

Step 1: Concept:
The question asks us to rank four of the seven basic crystal systems based on the number of valid 3D Bravais lattices associated with each system, sorted from highest to lowest.

Step 2: Key Formula or Approach:
There are 14 unique Bravais lattices distributed among 7 crystal systems. We need to recall the distribution:
1. Cubic: 3 lattices (Simple, Body-Centered, Face-Centered)
2. Tetragonal: 2 lattices (Simple, Body-Centered)
3. Orthorhombic: 4 lattices (Simple, Base-Centered, Body-Centered, Face-Centered)
4. Hexagonal: 1 lattice (Simple)
5. Rhombohedral (Trigonal): 1 lattice (Simple)
6. Monoclinic: 2 lattices (Simple, Base-Centered)
7. Triclinic: 1 lattice (Simple)

Step 3: Step-by-step Explanation:

• Let's assign the number of lattices to each given option:
A. Triclinic = 1 lattice
B. Orthorhombic = 4 lattices
C. Tetragonal = 2 lattices
D. Cubic = 3 lattices

• The question asks for the decreasing order (highest to lowest).

• Ranking the numbers: $4 > 3 > 2 > 1$.

• Mapping this back to the letters: B (Orthorhombic) > D (Cubic) > C (Tetragonal) > A (Triclinic).

Step 4: Final Answer:
The correct decreasing order is B, D, C, A, which corresponds to option (D).