If all the three interaxial angles defining the unit ceil are equal in magnitude, the crystal cannot be!ong to
(I) Orthorhombic system
(II) Monoclinic system
(III) Hexagonal system
(IV) Tetragonal system

Options

A. II, III
B. I, IV
C. III, IV
D. I, II

Answer

To solve the question, we need to analyze the interaxial angles of the different crystal systems mentioned: Orthorhombic, Monoclinic, Hexagonal, and Tetragonal.

### Step 1: Understand the Interaxial Angles
The interaxial angles (α, β, γ) define the geometry of the unit cell in crystal systems:
- **Orthorhombic system**: α = β = γ = 90°
- **Monoclinic system**: α = γ = 90°, β ≠ 90°
- **Hexagonal system**: α = β = 90°, γ = 120°
- **Tetragonal system**: α = β = γ = 90°

### Step 2: Identify the Condition
The question states that all three interaxial angles are equal in magnitude. This means we are looking for a system where α = β = γ.

### Step 3: Analyze Each System
1. **Orthorhombic**: All angles are equal (90°). This system can have equal angles.
2. **Monoclinic**: Two angles are equal (90°), but one is not. This system cannot have all three angles equal.
3. **Hexagonal**: Two angles are equal (90°), and one is 120°. This system cannot have all three angles equal.
4. **Tetragonal**: All angles are equal (90°). This system can have equal angles.

### Step 4: Conclusion
From the analysis, the Monoclinic and Hexagonal systems cannot have all three angles equal. However, the question asks for the system that cannot belong to the condition of all angles being equal.

Since the Monoclinic system is the only one where two angles are equal and one is not, it is the correct answer.

### Final Answer
The crystal cannot belong to the **Monoclinic system**.

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