Axial distances are `a = bne c` and axial angles are `a = 90^(0) = beta, Y = 120^(@)` in the system

Options

A. hexagonal
B. tetragonal
C. cubic
D. monoclinic

Answer

To determine the crystal system based on the given axial distances and angles, we can follow these steps:

### Step 1: Identify the Axial Distances
The axial distances are given as:
- \( a = b \neq c \)

This indicates that two of the axes (a and b) are equal, while the third axis (c) is different.

### Step 2: Identify the Axial Angles
The axial angles are given as:
- \( \alpha = 90^\circ \)
- \( \beta = 90^\circ \)
- \( \gamma = 120^\circ \)

This means that the angles between the axes are specific, with two angles being right angles (90 degrees) and one angle being 120 degrees.

### Step 3: Compare with Crystal Systems
Now, we compare the given parameters with known crystal systems:

1. **Hexagonal System**:
- Two axial distances are equal (like \( a = b \)).
- Axial angles: \( \alpha = 90^\circ \), \( \beta = 90^\circ \), \( \gamma = 120^\circ \).

2. **Tetragonal System**:
- Two axial distances are equal (like \( a = b \)).
- Axial angles: All angles are \( 90^\circ \).

3. **Cubic System**:
- All axial distances are equal (like \( a = b = c \)).
- All angles are \( 90^\circ \).

4. **Monoclinic System**:
- Axial distances can be different.
- Two angles are \( 90^\circ \) and one angle is not \( 90^\circ \) or \( 120^\circ \).

### Step 4: Conclusion
Given the conditions:
- \( a = b \neq c \)
- \( \alpha = 90^\circ \), \( \beta = 90^\circ \), \( \gamma = 120^\circ \)

The only system that matches these criteria is the **Hexagonal System**.

### Final Answer
The correct answer is **Hexagonal**.

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