The crystal system of a compound with unit cell dimensions `a=0.350,b=0.350` and `c=0.500` and `alpha=beta=90^(@)` and `gamma=120^(@)`is

Options

A. Cubic
B. Hexagonal
C. Orthorhombic
D. Rombohedral

Explanation

To determine the crystal system of the given compound based on the provided unit cell dimensions and angles, we can follow these steps:

### Step 1: Identify the given parameters
- Unit cell dimensions:
- \( a = 0.350 \)
- \( b = 0.350 \)
- \( c = 0.500 \)
- Angles:
- \( \alpha = 90^\circ \)
- \( \beta = 90^\circ \)
- \( \gamma = 120^\circ \)

### Step 2: Analyze the relationships between the dimensions
From the unit cell dimensions, we observe:
- \( a = b \) (both are equal)
- \( c \) is different from \( a \) and \( b \) (i.e., \( c \neq a \) and \( c \neq b \))

### Step 3: Analyze the angles
The angles provided are:
- \( \alpha = 90^\circ \)
- \( \beta = 90^\circ \)
- \( \gamma = 120^\circ \)

### Step 4: Determine the type of crystal system
Now, we can classify the crystal system based on the relationships between the sides and angles:

1. **Cubic**: All sides are equal and all angles are \( 90^\circ \). This does not fit our case since \( c \) is different.

2. **Rhombohedral**: All sides are equal but angles are not \( 90^\circ \). This does not fit our case since \( a \) and \( b \) are equal but \( c \) is different.

3. **Orthorhombic**: All sides are different. This does not fit our case since \( a \) and \( b \) are equal.

4. **Hexagonal**: Two sides are equal (\( a = b \)) and the third side is different (\( c \)). The angles are \( \alpha = \beta = 90^\circ \) and \( \gamma = 120^\circ \), which fits the hexagonal system.

### Conclusion
Based on the analysis, the crystal system of the compound is **Hexagonal**.

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