Question

There is NO base-centered cubic lattice among the list of 14 Bravais lattices because of one or more of the following reasons:

• A. It does NOT have translational symmetry
• B. It is only compatible with the symmetry of orthorhombic crystal system
• C. It is only compatible with the symmetry of tetragonal crystal system
• D. It does NOT have 3-fold rotation axes along the body diagonals

Hint:

Out of 14 Bravais lattices, cubic has only P, I, F. A base-centered cubic lattice is excluded because it destroys cubic symmetry (no 3-fold rotational axes).

Answer 1

The Correct Option is C, D

Step 1: Recall Bravais lattices.
There are 14 distinct Bravais lattices in 3D. Each corresponds to a unique combination of lattice system + centering that satisfies symmetry requirements. In cubic crystals, allowed Bravais lattices are: - Simple cubic (P), - Body-centered cubic (I), - Face-centered cubic (F).

Step 2: Why not base-centered cubic?
If we try to construct a base-centered cubic (C-centered), it would break cubic symmetry because: - Cubic system requires 3-fold rotation axes along body diagonals. - A base-centered lattice would not preserve this requirement. Thus, base-centered cubic is not a valid Bravais lattice.

Step 3: Verify options.
- (A): Wrong — it does have translational symmetry, but symmetry is incompatible. - (B): Wrong — orthorhombic system can have base-centered, but not cubic. - (C): Wrong — tetragonal system allows base-centering, but question is about cubic. - (D): Correct — cubic must have 3-fold rotation symmetry along body diagonals, which base-centering does not support. Final Answer:
\[ \boxed{\text{It does NOT have 3-fold rotation axes along the body diagonals.}} \]