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Which one of the following pairs of axis lengths (a, b, c) and inter-axial angles (α,β, γ) represents the tetragonal crystal system?  
  • a)
    a = b = c;α = β = γ = 900
  • b)
    a = b ≠ c;α = β = γ = 900
  • c)
    a ≠ b ≠ c;α = β = γ = 900
  • d)
    a = b = c;α = β = γ ≠ 900
Correct answer is option 'B'. Can you explain this answer?
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Understanding Tetragonal Crystal System
The tetragonal crystal system is one of the seven crystal systems in crystallography. It is characterized by specific relationships between the lengths of its axes and the angles between them.
Key Characteristics of Tetragonal System
- Axis Lengths: In a tetragonal crystal system, two axes are of equal length, while the third axis is of a different length. This can be summarized as:
- a = b ≠ c
- Inter-Axial Angles: All angles between the axes are right angles (90 degrees). Therefore, the angles can be defined as:
- α = β = γ = 90°
Analyzing the Options
- Option A: a = b = c; α = β = γ = 90°
- This describes a cubic system, not tetragonal.
- Option B: a = b ≠ c; α = β = γ = 90°
- This correctly represents the tetragonal system, as it has two equal axes and one different.
- Option C: a ≠ b ≠ c; α = β = γ = 90°
- This describes an orthorhombic system, where all axes are of different lengths.
- Option D: a = b = c; α = β = 90°
- This again describes a cubic system.
Conclusion
The correct answer is indeed Option B: a = b ≠ c; α = β = γ = 90°, accurately representing the characteristics of the tetragonal crystal system.
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