Which of the following systems is not correctly characterised ?

Options

A. cubic : `a=b=c, alpha=beta=gamma=90^(@)`
B. tetragonal : `a=b ne c, alpha=beta =gamma=90^(@)`
C. orthorhombic : `a ne b ne c, alpha = beta = gamma=90^(@)`
D. rhombohedral : `a=bnec : alpha=beta=gamma=90^(@)`

Answer

To solve the question of which system is not correctly characterized, we need to analyze the characteristics of the rhombohedral system in crystallography.

### Step-by-Step Solution:

1. **Understand the Rhombohedral System**:
- In a rhombohedral crystal system, the lengths of the edges (a, b, c) are not all equal. Specifically, it is characterized by:
- \( a \neq b \neq c \)
- The angles (α, β, γ) are equal, but none of them are 90 degrees:
- \( \alpha = \beta = \gamma \) and \( \alpha, \beta, \gamma \neq 90^\circ \)

2. **Analyze the Given Options**:
- We need to check the options provided in the question to see which one does not match the characteristics of the rhombohedral system.
- One of the options states:
- \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \)
- This option suggests that two edges are equal and all angles are 90 degrees, which is characteristic of a cubic system, not a rhombohedral system.

3. **Identify the Incorrect Characterization**:
- Since the characteristics of the rhombohedral system were not met in the option that states \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \), we conclude that this option is incorrectly characterized.

4. **Final Answer**:
- The system that is not correctly characterized is the one that states \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \).