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Which has no rotation of symmetry ?...

Which has no rotation of symmetry ?

A

hexagonal

B

Orthochromic

C

Cubic

D

Triclinic

Text Solution

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The correct Answer is:
To determine which of the given crystal systems has no rotation of symmetry, we can analyze the properties of each system: 1. **Hexagonal System**: - Edge lengths: \( A_1 = A_2 \neq A_3 \) - Interfacial angles: \( \alpha = \beta = 90^\circ \), \( \gamma = 120^\circ \) - **Symmetry**: This system has some rotational symmetry due to the equal edge lengths and angles. 2. **Orthorhombic System**: - Edge lengths: \( A_1 \neq A_2 \neq A_3 \) - Interfacial angles: \( \alpha = \beta = \gamma = 90^\circ \) - **Symmetry**: This system also has rotational symmetry as all angles are equal. 3. **Cubic System**: - Edge lengths: \( A_1 = A_2 = A_3 \) - Interfacial angles: \( \alpha = \beta = \gamma = 90^\circ \) - **Symmetry**: The cubic system is the most symmetric of all, having full rotational symmetry. 4. **Triclinic System**: - Edge lengths: \( A_1 \neq A_2 \neq A_3 \) - Interfacial angles: \( \alpha \neq \beta \neq \gamma \) - **Symmetry**: This system has no symmetry, making it the most asymmetric. Based on the analysis, the crystal system that has no rotation of symmetry is the **Triclinic System**. ### Final Answer: The crystal system that has no rotation of symmetry is **Triclinic**.
To determine which of the given crystal systems has no rotation of symmetry, we can analyze the properties of each system: 1. **Hexagonal System**: - Edge lengths: \( A_1 = A_2 \neq A_3 \) - Interfacial angles: \( \alpha = \beta = 90^\circ \), \( \gamma = 120^\circ \) - **Symmetry**: This system has some rotational symmetry due to the equal edge lengths and angles. 2. **Orthorhombic System**: ...
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