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The crystal system for which a!= b!= c a...

The crystal system for which `a!= b!= c and alpha = beta = gamma = 90^(@)` is said to be

A

Cubic

B

Tetragonal

C

Orthorhombic

D

Hexagonal

Text Solution

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The correct Answer is:
To solve the question regarding the crystal system characterized by the conditions \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \), we will analyze the properties of different crystal systems step by step. ### Step-by-Step Solution: 1. **Understanding the Given Conditions:** - We are given that the lengths of the edges of the crystal unit cell are not equal: \( a \neq b \neq c \). - We also know that the angles between the edges are all equal to \( 90^\circ \): \( \alpha = \beta = \gamma = 90^\circ \). 2. **Identifying Crystal Systems:** - There are seven crystal systems in total: 1. Cubic 2. Tetragonal 3. Orthorhombic 4. Hexagonal 5. Triclinic 6. Monoclinic 7. Rhombohedral 3. **Analyzing Each Crystal System:** - **Cubic:** In cubic systems, \( a = b = c \) and \( \alpha = \beta = \gamma = 90^\circ \). This does not satisfy our conditions. - **Tetragonal:** In tetragonal systems, \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \). This does not satisfy our conditions either. - **Hexagonal:** In hexagonal systems, \( a = b \neq c \) but \( \gamma = 120^\circ \). This does not satisfy our conditions. - **Orthorhombic:** In orthorhombic systems, \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \). This satisfies our conditions perfectly. - **Triclinic:** In triclinic systems, \( a \neq b \neq c \) and \( \alpha, \beta, \gamma \) are all different from \( 90^\circ \). This does not satisfy our conditions. - **Monoclinic:** In monoclinic systems, \( a \neq b \neq c \) but one of the angles (either \( \alpha \) or \( \beta \) or \( \gamma \)) is not \( 90^\circ \). This does not satisfy our conditions. - **Rhombohedral:** In rhombohedral systems, \( a = b = c \) but angles are not \( 90^\circ \). This does not satisfy our conditions. 4. **Conclusion:** - The only crystal system that meets the criteria of \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \) is the **Orthorhombic** system. ### Final Answer: The crystal system for which \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \) is **Orthorhombic**.
To solve the question regarding the crystal system characterized by the conditions \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \), we will analyze the properties of different crystal systems step by step. ### Step-by-Step Solution: 1. **Understanding the Given Conditions:** - We are given that the lengths of the edges of the crystal unit cell are not equal: \( a \neq b \neq c \). - We also know that the angles between the edges are all equal to \( 90^\circ \): \( \alpha = \beta = \gamma = 90^\circ \). ...
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