Question
Download Solution PDFWhich primitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles different from 90° ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Primitive Unit Cells and Their Characteristics
- Unit cells are classified based on the lengths of their edges (a, b, c) and the angles between them (α, β, γ).
- The different crystal systems are characterized as follows:
| Crystal System | Edge Lengths | Axial Angles |
|---|---|---|
| Monoclinic | a ≠ b ≠ c | α = γ = 90°; β ≠ 90° |
| Tetragonal | a = b ≠ c | α = β = γ = 90° |
| Triclinic | a ≠ b ≠ c | α ≠ β ≠ γ ≠ 90° |
| Hexagonal | a = b ≠ c | α = β = 90°; γ = 120° |
EXPLANATION:
- Option 1: Monoclinic has unequal edge lengths (a ≠ b ≠ c) but only one angle differs from 90°.
- Option 2: Tetragonal has two equal edge lengths (a = b ≠ c) and all angles are 90°.
- Option 3: Triclinic has unequal edge lengths (a ≠ b ≠ c) and all angles are different from 90° (α ≠ β ≠ γ ≠ 90°).
- Option 4: Hexagonal has two equal edge lengths (a = b ≠ c) with specific angles (α = β = 90°; γ = 120°).
The correct answer is (3) Triclinic.
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