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 properties of the different crystal systems based on their interaxial angles.

### Step-by-Step Solution:

1. **Understanding Interaxial Angles**:
- In crystallography, the unit cell is defined by three axes (a, b, c) and the angles between them (α, β, γ).
- The angles can be equal or unequal depending on the type of crystal system.

2. **Identifying the Conditions**:
- The question states that all three interaxial angles (α, β, γ) are equal. This means α = β = γ.

3. **Analyzing Crystal Systems**:
- **Cubic System**: In cubic crystals, all angles are equal (α = β = γ = 90°). Therefore, a cubic crystal can have equal interaxial angles.
- **Tetragonal System**: In tetragonal crystals, the angles are also equal (α = β = γ = 90°). Thus, a tetragonal crystal can also have equal interaxial angles.
- **Orthorhombic System**: In orthorhombic crystals, the angles are equal (α = β = γ = 90°). Therefore, orthorhombic crystals can also have equal interaxial angles.
- **Monoclinic System**: In monoclinic crystals, only two angles are equal, while the third angle is different (α = γ ≠ β). Therefore, monoclinic crystals cannot have all three angles equal.
- **Hexagonal System**: In hexagonal crystals, two angles are equal (α = β ≠ γ), and the third angle is different. Thus, hexagonal crystals cannot have all three angles equal.

4. **Conclusion**:
- Since the question asks which crystal system cannot have all three interaxial angles equal, we find that the monoclinic and hexagonal systems cannot have α = β = γ.
- Therefore, the correct answer is **(II) Monoclinic system** and **(III) Hexagonal system**.

### Final Answer:
The crystal cannot belong to the **Monoclinic system (II)** and **Hexagonal system (III)**.

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